A new adaptive local mesh refinement algorithm and its application on fourth order thin film flow problem
A new adaptive local mesh refinement method is presented for thin film flow problems containing moving contact lines. Based on adaptation on an optimal interpolation error estimate in the Lp norm (1<p⩽∞) [L. Chen, P. Sun, J. Xu, Multilevel homotopic adaptive finite element methods for convection...
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| Veröffentlicht in: | Journal of computational physics Jg. 224; H. 2; S. 1021 - 1048 |
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| Abstract | A new adaptive local mesh refinement method is presented for thin film flow problems containing moving contact lines. Based on adaptation on an optimal interpolation error estimate in the Lp norm (1<p⩽∞) [L. Chen, P. Sun, J. Xu, Multilevel homotopic adaptive finite element methods for convection dominated problems, in: Domain Decomposition Methods in Science and Engineering, Lecture Notes in Computational Science and Engineering 40 (2004) 459–468], we obtain the optimal anisotropic adaptive meshes in terms of the Hessian matrix of the numerical solution. Such an anisotropic mesh is optimal for anisotropic solutions like the solution of thin film equations on moving contact lines. Thin film flow is described by an important type of nonlinear degenerate fourth order parabolic PDE. In this paper, we address the algorithms and implementation of the new adaptive finite element method for solving such fourth order thin film equations. By means of the resulting algorithm, we are able to capture and resolve the moving contact lines very precisely and efficiently without using any regularization method, even for the extreme degenerate cases, but with fewer grid points and degrees of freedom in contrast to methods on a fixed mesh. As well, we compare the method theoretically and computationally to the positivity-preserving finite difference scheme on a fixed uniform mesh which has proven useful for solving the thin film problem. |
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| AbstractList | A new adaptive local mesh refinement method is presented for thin film flow problems containing moving contact lines. Based on adaptation on an optimal interpolation error estimate in the Lp norm (1<p⩽∞) [L. Chen, P. Sun, J. Xu, Multilevel homotopic adaptive finite element methods for convection dominated problems, in: Domain Decomposition Methods in Science and Engineering, Lecture Notes in Computational Science and Engineering 40 (2004) 459–468], we obtain the optimal anisotropic adaptive meshes in terms of the Hessian matrix of the numerical solution. Such an anisotropic mesh is optimal for anisotropic solutions like the solution of thin film equations on moving contact lines. Thin film flow is described by an important type of nonlinear degenerate fourth order parabolic PDE. In this paper, we address the algorithms and implementation of the new adaptive finite element method for solving such fourth order thin film equations. By means of the resulting algorithm, we are able to capture and resolve the moving contact lines very precisely and efficiently without using any regularization method, even for the extreme degenerate cases, but with fewer grid points and degrees of freedom in contrast to methods on a fixed mesh. As well, we compare the method theoretically and computationally to the positivity-preserving finite difference scheme on a fixed uniform mesh which has proven useful for solving the thin film problem. A new adaptive local mesh refinement method is presented for thin film flow problems containing moving contact lines. Based on adaptation on an optimal interpolation error estimate in the Lp norm (1 < p{infinity}) [L. Chen, P. Sun, J. Xu, Multilevel homotopic adaptive finite element methods for convection dominated problems, in: Domain Decomposition Methods in Science and Engineering, Lecture Notes in Computational Science and Engineering 40 (2004) 459-468], we obtain the optimal anisotropic adaptive meshes in terms of the Hessian matrix of the numerical solution. Such an anisotropic mesh is optimal for anisotropic solutions like the solution of thin film equations on moving contact lines. Thin film flow is described by an important type of nonlinear degenerate fourth order parabolic PDE. In this paper, we address the algorithms and implementation of the new adaptive finite element method for solving such fourth order thin film equations. By means of the resulting algorithm, we are able to capture and resolve the moving contact lines very precisely and efficiently without using any regularization method, even for the extreme degenerate cases, but with fewer grid points and degrees of freedom in contrast to methods on a fixed mesh. As well, we compare the method theoretically and computationally to the positivity-preserving finite difference scheme on a fixed uniform mesh which has proven useful for solving the thin film problem. |
| Author | Sun, Pengtao Xu, Jinchao Russell, Robert D. |
| Author_xml | – sequence: 1 givenname: Pengtao surname: Sun fullname: Sun, Pengtao email: sun@math.psu.edu organization: Department of Mathematics, Simon Fraser University, USA – sequence: 2 givenname: Robert D. surname: Russell fullname: Russell, Robert D. email: rdr@math.sfu.ca organization: Department of Mathematics, Simon Fraser University, USA – sequence: 3 givenname: Jinchao surname: Xu fullname: Xu, Jinchao email: xu@math.psu.edu organization: Department of Mathematics, Simon Fraser University, USA |
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| CitedBy_id | crossref_primary_10_1007_s10915_012_9660_1 crossref_primary_10_1007_s11012_013_9788_6 crossref_primary_10_1016_j_cam_2017_01_019 crossref_primary_10_1016_j_euromechflu_2013_05_003 crossref_primary_10_1016_j_jcp_2013_01_052 crossref_primary_10_1016_j_amc_2018_06_017 crossref_primary_10_1016_j_jcp_2009_05_008 crossref_primary_10_1016_j_cam_2019_02_010 crossref_primary_10_1016_j_jcp_2011_04_029 crossref_primary_10_1007_s10915_009_9337_6 crossref_primary_10_1007_s00332_022_09844_3 crossref_primary_10_1016_j_sysconle_2008_03_017 |
| Cites_doi | 10.1006/jcph.2001.6945 10.1063/1.868800 10.1137/S0036142994265292 10.1090/S0025-5718-06-01896-5 10.1137/S0036141094267662 10.1090/S0025-5718-03-01600-4 10.1016/S0167-2789(97)00066-3 10.1038/346824a0 10.1002/(SICI)1097-0312(199602)49:2<85::AID-CPA1>3.0.CO;2-2 10.1103/PhysRevE.47.4169 10.1007/s002110050377 10.1038/300427a0 10.1090/S0025-5718-99-01205-3 10.1007/s007910050015 10.1103/PhysRevLett.62.1496 10.1137/0912040 10.2172/414390 10.1002/nme.1620330702 10.1017/S0956792501004466 10.1016/S0021-9991(02)00040-2 10.1137/0715049 10.1017/S0956792501004429 10.1103/PhysRevE.63.011208 10.1063/1.868263 10.1002/nme.1620320406 10.1137/S0036144502409093 10.1007/s002110100273 10.1063/1.869217 10.1137/0910064 10.1063/1.858351 10.1137/S0036142901398751 10.1209/0295-5075/10/1/005 10.1016/S0168-9274(02)00194-0 10.1137/S003614290139874X 10.1002/cnm.1630040603 10.1002/nme.1620330703 10.1080/00036817408839073 10.1137/0733054 10.4171/ZAA/639 10.1007/BF00379920 10.1016/0899-8248(90)90003-S 10.1017/S0956792500002369 10.1006/jcph.2002.7197 10.1002/(SICI)1098-2426(199903)15:2<151::AID-NUM2>3.0.CO;2-O 10.1063/1.865410 10.1006/tpbi.1994.1014 10.1088/0953-8984/17/9/002 10.1017/S0022112078000075 10.1137/S0036139994271972 10.1137/S003614450240135 10.1137/S0036142998335698 10.1063/1.1409965 10.1016/0022-0396(90)90074-Y 10.1007/3-540-26825-1_47 10.1063/1.868915 10.1137/0721042 10.1017/S0956792599003769 |
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| Keywords | Adaptive mesh Mixed finite element method Local refinement Moving contact lines Thin film flow Degrees of freedom Difference scheme Partial differential equations Decomposition method Adaptive method Sun Convection Calculation methods Thin films Regularization method Finite element method Algorithms Numerical solution Optimal solution Optimal approximation Calculation Mesh method |
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| References | Lewis (bib58) 1994; 45 Bertozzi, Münch, Shearer, Zumbrun (bib15) 2001; 12 Zienkiewicz, Zhu (bib80) 1992; 33 D’Azevedo (bib32) 1991; 12 Troian, Wu, Safran (bib69) 1989; 62 Cazabat, Heslot, Troian, Carles (bib24) 1990; 346 Grün (bib46) 1995; 14 Zienkiewicz, Zhu (bib79) 1992; 33 de Boor (bib34) 1973; vol. 21 Elliott, Garcke (bib39) 1996; 27 Nadler (bib62) 1986; V Kondic, Diez (bib54) 2001; 13 Zhang (bib75) 1999; 69 F. Bernis, Viscous flows, fourth order nonlinear degenerate parabolic equations and singular elliptic problems, in free boundary problems: theory and applications, in: Pitman Research Notes in Mathematics, vol. 323, 1995, pp. 40–56. Grün, Rumpf (bib47) 2001; 12 Elliott, Garcke (bib40) 1997; 109 Carles, Cazabat (bib23) 1990; 248 de Boor (bib33) 1974; vol. 363 Diez, Kondic (bib35) 2002; 183 Diez, Kondic, Bertozzi (bib36) 2000; 63 Kondic (bib53) 2003; 45 Huang (bib49) 2001; 174 Chen, Sun, Xu (bib28) 2007; 76 Rivara (bib64) 1984; 21 Constantin, Dupont, Goldstein, Kadanoff, Shelley, Zhou (bib29) 1993; 47 G. Kunert, A a posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes, Ph.D. Thesis, 1999. Jerrett, Bruyn (bib52) 1992; 4 Verfürth (bib71) 1996 L.A. Freitag, M.T. Jones, P.E. Plassmann, An efficient parallel algorithm for mesh smoothing, in: Proceedings of the 4th International Meshing Roundtables, Sandia Labs, 1995, pp. 47–58. Bertozzi, Pugh (bib16) 1996; 49 L. Chen, Robust and accurate algorithms for solving anisotropic singularities, Ph.D. thesis, Pennsylvania State University, 2005. Bertozzi (bib14) 1995; vol. 323 Xu, Zhang (bib74) 2004; 73 Bertozzi, Brenner, Dupont, Kadanoff (bib19) 1994; vol. 100 Greenspan (bib45) 1978; 84 Bertozzi (bib17) 1996; 56 Zhornitskaya, Bertozzi (bib78) 2000; 37 W.G. Habashi, M. Fortin, J. Dompierre, M. Vallet, D. Ati-Ali-Yahia, Y. Bourgault, M.P. Robichaud, A. Tam, S. Boivin, Anisotropic mesh optimization for structured and unstructured meshes, in: Proceedings of the 28th Computational Fluid Dynamics Lecture Series, von Karman Institute, March 1997. N.A. Zhang Z, A meshless gradient recovery method, part i: superconvergence recovery. Research Report #2, Department of Mathematics, Wayne State University, 2002. Field (bib41) 1988; 4 D’Azevedo, Simpson (bib31) 1989; 6 Dolejsi (bib70) 1998; vol. 1 Münch, Wagner (bib61) 1999; 10 Becker, Grün (bib10) 2005; 17 Bernis, Friedman (bib13) 1990; 83 Huang, Sun (bib50) 2003; 184 Witelski, Bowen (bib73) 2003; 45 Babuška, Rheinboldt (bib3) 1978; 15 Morin, Nochetto, Siebert (bib60) 2002; 44 L. Chen, P. Sun, J. Xu, Multilevel homotopic adaptive finite element methods for convection dominated problems, in: Domain Decomposition Methods in Science and Engineering, Lecture Notes in Computational Science and Engineering 40 (2004) 459–468. Lawson (bib57) 1977 D’Azevedo (bib30) 1991; 12 T. Apel, Anisotropic finite elements: local estimates and applications, in: J.P. Pier (Ed.), Advances in Numerical Mathematics, Stuttgart: Teubner 1999, Birkhauser, 1999. N.A. Zhang Z, A posteriori error estimates based on polynomial preserving recovery. Research Report #9, Department of Mathematics, Wayne State University, 2002. Li, Zhang (bib59) 1999; 15 Barrett, Blowey, Garcke (bib9) 1998; 80 Burchard (bib21) 1974; 3 Chen, Huang (bib25) 1995 Shephard, Georges (bib65) 1991; 32 Dörfler (bib38) 1996; 33 Bank, Xu (bib8) 2003; 41 Raviart, Thomas (bib63) 1977; vol. 606 Beretta, Berstch, Passo (bib11) 1995; 129 Babuška, Strouboulis (bib4) 2001 Formaggia, Perotto (bib42) 2001; 89 Fraysse, Homsy (bib43) 1994; 6 Bank, Smith (bib6) 1997; 34 Dolejsi (bib37) 1998; 1 Almgren, Bertozzi, Brenner (bib1) 1996; 8 Bertozzi, Brenner (bib18) 1997; 9 Troian, Herbolzheimer, Safran, Joanny (bib68) 1989; 10 Huppert (bib51) 1982; 300 Cahn, Elliott, Novick-Cohen (bib22) 1996; 7 Bank, Sherman, Weiser (bib5) 1983 Spaid, Homsy (bib67) 1996; 8 Wahlbin (bib72) 1995 Bank, Xu (bib7) 2003; 41 Borouchaki, Castro-Diaz, George, Hecht, Mohammadi (bib20) 1996; vol. 3 Kornhuber, Roitzsch (bib55) 1990; 2 Silvi, Dussan (bib66) 1985; 28 Huang (10.1016/j.jcp.2006.11.005_bib49) 2001; 174 10.1016/j.jcp.2006.11.005_bib76 D’Azevedo (10.1016/j.jcp.2006.11.005_bib32) 1991; 12 Elliott (10.1016/j.jcp.2006.11.005_bib40) 1997; 109 Kondic (10.1016/j.jcp.2006.11.005_bib53) 2003; 45 Field (10.1016/j.jcp.2006.11.005_bib41) 1988; 4 10.1016/j.jcp.2006.11.005_bib77 Becker (10.1016/j.jcp.2006.11.005_bib10) 2005; 17 Constantin (10.1016/j.jcp.2006.11.005_bib29) 1993; 47 Beretta (10.1016/j.jcp.2006.11.005_bib11) 1995; 129 D’Azevedo (10.1016/j.jcp.2006.11.005_bib31) 1989; 6 Dolejsi (10.1016/j.jcp.2006.11.005_bib37) 1998; 1 Li (10.1016/j.jcp.2006.11.005_bib59) 1999; 15 Raviart (10.1016/j.jcp.2006.11.005_bib63) 1977; vol. 606 Chen (10.1016/j.jcp.2006.11.005_bib25) 1995 Bertozzi (10.1016/j.jcp.2006.11.005_bib19) 1994; vol. 100 Verfürth (10.1016/j.jcp.2006.11.005_bib71) 1996 Wahlbin (10.1016/j.jcp.2006.11.005_bib72) 1995 Barrett (10.1016/j.jcp.2006.11.005_bib9) 1998; 80 Zhang (10.1016/j.jcp.2006.11.005_bib75) 1999; 69 de Boor (10.1016/j.jcp.2006.11.005_bib33) 1974; vol. 363 Shephard (10.1016/j.jcp.2006.11.005_bib65) 1991; 32 Grün (10.1016/j.jcp.2006.11.005_bib46) 1995; 14 Nadler (10.1016/j.jcp.2006.11.005_bib62) 1986; V Carles (10.1016/j.jcp.2006.11.005_bib23) 1990; 248 Zienkiewicz (10.1016/j.jcp.2006.11.005_bib80) 1992; 33 Almgren (10.1016/j.jcp.2006.11.005_bib1) 1996; 8 Bertozzi (10.1016/j.jcp.2006.11.005_bib14) 1995; vol. 323 Witelski (10.1016/j.jcp.2006.11.005_bib73) 2003; 45 10.1016/j.jcp.2006.11.005_bib27 de Boor (10.1016/j.jcp.2006.11.005_bib34) 1973; vol. 21 10.1016/j.jcp.2006.11.005_bib26 Formaggia (10.1016/j.jcp.2006.11.005_bib42) 2001; 89 Lawson (10.1016/j.jcp.2006.11.005_bib57) 1977 Cazabat (10.1016/j.jcp.2006.11.005_bib24) 1990; 346 Xu (10.1016/j.jcp.2006.11.005_bib74) 2004; 73 Lewis (10.1016/j.jcp.2006.11.005_bib58) 1994; 45 Bank (10.1016/j.jcp.2006.11.005_bib7) 2003; 41 Bertozzi (10.1016/j.jcp.2006.11.005_bib16) 1996; 49 Dörfler (10.1016/j.jcp.2006.11.005_bib38) 1996; 33 Diez (10.1016/j.jcp.2006.11.005_bib36) 2000; 63 D’Azevedo (10.1016/j.jcp.2006.11.005_bib30) 1991; 12 10.1016/j.jcp.2006.11.005_bib12 10.1016/j.jcp.2006.11.005_bib56 Bank (10.1016/j.jcp.2006.11.005_bib5) 1983 Bertozzi (10.1016/j.jcp.2006.11.005_bib15) 2001; 12 Zhornitskaya (10.1016/j.jcp.2006.11.005_bib78) 2000; 37 Bank (10.1016/j.jcp.2006.11.005_bib6) 1997; 34 Kornhuber (10.1016/j.jcp.2006.11.005_bib55) 1990; 2 Silvi (10.1016/j.jcp.2006.11.005_bib66) 1985; 28 Diez (10.1016/j.jcp.2006.11.005_bib35) 2002; 183 Rivara (10.1016/j.jcp.2006.11.005_bib64) 1984; 21 Troian (10.1016/j.jcp.2006.11.005_bib69) 1989; 62 Dolejsi (10.1016/j.jcp.2006.11.005_bib70) 1998; vol. 1 Burchard (10.1016/j.jcp.2006.11.005_bib21) 1974; 3 Elliott (10.1016/j.jcp.2006.11.005_bib39) 1996; 27 Greenspan (10.1016/j.jcp.2006.11.005_bib45) 1978; 84 Babuška (10.1016/j.jcp.2006.11.005_bib4) 2001 Fraysse (10.1016/j.jcp.2006.11.005_bib43) 1994; 6 10.1016/j.jcp.2006.11.005_bib2 Troian (10.1016/j.jcp.2006.11.005_bib68) 1989; 10 Borouchaki (10.1016/j.jcp.2006.11.005_bib20) 1996; vol. 3 Grün (10.1016/j.jcp.2006.11.005_bib47) 2001; 12 Bertozzi (10.1016/j.jcp.2006.11.005_bib18) 1997; 9 Jerrett (10.1016/j.jcp.2006.11.005_bib52) 1992; 4 Münch (10.1016/j.jcp.2006.11.005_bib61) 1999; 10 10.1016/j.jcp.2006.11.005_bib44 Bank (10.1016/j.jcp.2006.11.005_bib8) 2003; 41 Huang (10.1016/j.jcp.2006.11.005_bib50) 2003; 184 10.1016/j.jcp.2006.11.005_bib48 Kondic (10.1016/j.jcp.2006.11.005_bib54) 2001; 13 Zienkiewicz (10.1016/j.jcp.2006.11.005_bib79) 1992; 33 Bernis (10.1016/j.jcp.2006.11.005_bib13) 1990; 83 Huppert (10.1016/j.jcp.2006.11.005_bib51) 1982; 300 Cahn (10.1016/j.jcp.2006.11.005_bib22) 1996; 7 Morin (10.1016/j.jcp.2006.11.005_bib60) 2002; 44 Babuška (10.1016/j.jcp.2006.11.005_bib3) 1978; 15 Chen (10.1016/j.jcp.2006.11.005_bib28) 2007; 76 Bertozzi (10.1016/j.jcp.2006.11.005_bib17) 1996; 56 Spaid (10.1016/j.jcp.2006.11.005_bib67) 1996; 8 |
| References_xml | – volume: 174 start-page: 903 year: 2001 end-page: 924 ident: bib49 article-title: Variational mesh adaptation: isotropy and equidistribution publication-title: J. Comput. Phys. – reference: N.A. Zhang Z, A meshless gradient recovery method, part i: superconvergence recovery. Research Report #2, Department of Mathematics, Wayne State University, 2002. – volume: 184 start-page: 619 year: 2003 end-page: 648 ident: bib50 article-title: Variational mesh adaptation II: error estimates and monitor functions publication-title: J. Comput. Phys. – year: 1996 ident: bib71 article-title: A review of a posteriori error estimation and adaptive mesh-refinement techniques – volume: 1 start-page: 165 year: 1998 end-page: 178 ident: bib37 article-title: Anisotropic mesh adaptation for finite volume and finite element methods on triangular meshes publication-title: Comput. Visual. Sci. – volume: 49 start-page: 85 year: 1996 end-page: 123 ident: bib16 article-title: The lubrication approximation for thin viscous films: regularity and long time behaviour of weak solutions publication-title: Commun. Pure Appl. Math. – year: 2001 ident: bib4 article-title: The finite element method and its reliability publication-title: Numerical Mathematics and Scientific Computation – volume: 89 start-page: 641 year: 2001 end-page: 667 ident: bib42 article-title: New anisotropic a priori error estimates publication-title: Numer. Math. – volume: 44 start-page: 631 year: 2002 end-page: 658 ident: bib60 article-title: Convergence of adaptive finite element methods publication-title: SIAM Rev. – volume: 69 start-page: 141 year: 1999 end-page: 158 ident: bib75 article-title: Ultraconvergence of the patch recovery technique II publication-title: Math. Comp. – volume: 346 start-page: 824 year: 1990 end-page: 826 ident: bib24 article-title: Finger instability of this spreading films driven by temperature gradients publication-title: Nature – volume: 21 start-page: 604 year: 1984 end-page: 613 ident: bib64 article-title: Mesh refinement processes based on the generalized bisection of simplices publication-title: SIAM J. Numer. Anal. – volume: vol. 21 year: 1973 ident: bib34 publication-title: Good Approximation by Splines with Variable Knots – volume: 28 start-page: 5 year: 1985 end-page: 7 ident: bib66 article-title: On the rewetting of an inclined solid surface by a liquid publication-title: Phys. Fluids – volume: vol. 100 year: 1994 ident: bib19 article-title: Singularities and similarities in interface flow publication-title: Trends and Perspectives in Applied Mathematics – reference: L. Chen, Robust and accurate algorithms for solving anisotropic singularities, Ph.D. thesis, Pennsylvania State University, 2005. – reference: N.A. Zhang Z, A posteriori error estimates based on polynomial preserving recovery. Research Report #9, Department of Mathematics, Wayne State University, 2002. – volume: 34 start-page: 979 year: 1997 end-page: 997 ident: bib6 article-title: Mesh smoothing using a posteriori error estimates publication-title: SIAM J. Numer. Anal. – volume: 63 start-page: 011208-1 year: 2000 end-page: 011208-13 ident: bib36 article-title: Global models for moving contact lines publication-title: Phys. Rev. E – volume: vol. 323 year: 1995 ident: bib14 article-title: Loss and gain of regularity in a lubrication equation for thin viscous films, in Free boundary problems: theory and applications publication-title: Pitman Research Notes in Mathematics – volume: 8 start-page: 460 year: 1996 end-page: 478 ident: bib67 article-title: Stability of newtonian and viscoelastic dynamic contact line publication-title: Phys. Fluids – volume: 248 year: 1990 ident: bib23 article-title: On the origin of the bump in the profile of surface-tension-gradient-driven spreading films publication-title: Mat. Res. Soc. Symp. Proc. – volume: 76 start-page: 179 year: 2007 end-page: 204 ident: bib28 article-title: Optimal anisotropic simplicial meshes for minimizing interpolation errors in publication-title: Math. Comp. – volume: 62 start-page: 1496 year: 1989 end-page: 1499 ident: bib69 article-title: Fingering instability in thin wetting films publication-title: Phys. Rev. Lett. – volume: 41 start-page: 2294 year: 2003 end-page: 2312 ident: bib7 article-title: Asymptotically exact a posteriori error estimators, part I: grids with superconvergence publication-title: SIAM J. Numer. Anal. – volume: vol. 606 year: 1977 ident: bib63 article-title: A mixed finite element method for 2nd order elliptic problems publication-title: Mathematical Aspects of the Finite Element Method – volume: 4 start-page: 234 year: 1992 end-page: 242 ident: bib52 article-title: Finger instability of a gravitationally driven contact line publication-title: Phys. Fluids A – volume: 13 start-page: 3168 year: 2001 end-page: 3184 ident: bib54 article-title: Pattern formation in the flow of thin films down an incline:constant flux configuration publication-title: Phys. Fluids – volume: 15 start-page: 736 year: 1978 end-page: 754 ident: bib3 article-title: Error estimates for adaptive finite element computations publication-title: SIAM J. Numer. Anal. – volume: 45 start-page: 277 year: 1994 ident: bib58 article-title: Spatial coupling of plant and herbivore dynamics: the contribution of herbivore dispersal to transient and persistent waves of damage publication-title: Theor. Popul. Biol. – volume: 33 start-page: 1331 year: 1992 end-page: 1364 ident: bib79 article-title: The superconvergence patch recovery and a posteriori error estimates. part 1: the recovery techniques publication-title: Internat. J. Numer. Method Eng. – volume: 14 start-page: 541 year: 1995 end-page: 574 ident: bib46 article-title: Degenerate parabolic differential equations of fourth order and a plasticity model with nonlocal hardening publication-title: Z. Anal. Anwend. – volume: 300 start-page: 427 year: 1982 end-page: 429 ident: bib51 article-title: Flow and instability of a viscous current down a slope publication-title: Nature – volume: V start-page: 499 year: 1986 end-page: 502 ident: bib62 article-title: Piecewise linear best publication-title: Approx. Theory – volume: 12 start-page: 755 year: 1991 end-page: 786 ident: bib32 article-title: Optimal triangular mesh generation by coordinate transformation publication-title: SIAM J. Sci. Stat. Comp. – volume: 183 start-page: 274 year: 2002 end-page: 306 ident: bib35 article-title: Computing three-dimensional thin film flows including contact lines publication-title: J. Comp. Phys. – volume: 45 start-page: 331 year: 2003 end-page: 351 ident: bib73 article-title: ADI schemes for higher-order nonlinear diffusion equations publication-title: Appl. Numer. Math. – volume: 3 start-page: 309 year: 1974 end-page: 319 ident: bib21 article-title: Splines (with optimal knots) are better publication-title: Appl. Anal. – volume: 33 start-page: 1106 year: 1996 end-page: 1124 ident: bib38 article-title: A convergent adaptive algorithm for poissons equation publication-title: SIAM J. Numer. Anal. – reference: T. Apel, Anisotropic finite elements: local estimates and applications, in: J.P. Pier (Ed.), Advances in Numerical Mathematics, Stuttgart: Teubner 1999, Birkhauser, 1999. – volume: 9 start-page: 530 year: 1997 end-page: 539 ident: bib18 article-title: Linear stability and transient growth in driven contact lines publication-title: Phys. Fluids – volume: 33 start-page: 1365 year: 1992 end-page: 1382 ident: bib80 article-title: The superconvergence patch recovery and a posteriori error estimates. part 2: error estimates and adaptivity publication-title: Int. J. Numer. Methods Eng. – volume: 45 start-page: 95 year: 2003 end-page: 115 ident: bib53 article-title: Instabilities in gravity driven flow of thin fluid publication-title: SIAM Rev. – volume: 56 start-page: 681 year: 1996 end-page: 714 ident: bib17 article-title: Symmetric singularity formation in lubrication-type equations for interface motion publication-title: SIAM J. Appl. Math. – volume: 10 start-page: 25 year: 1989 end-page: 30 ident: bib68 article-title: Fingering instabilities of driven spreading films publication-title: Europhys. Lett. – volume: vol. 3 start-page: 197 year: 1996 end-page: 206 ident: bib20 article-title: Anisotropic adaptive mesh generation in two dimensions for cfd publication-title: Proceedings of the 5th International Conference On Numerical Grid Generation in Computational Field Simulations – volume: 37 start-page: 523 year: 2000 end-page: 555 ident: bib78 article-title: Positivity preserving numerical schemes for lubrication-type equations publication-title: SIAM J. Numer. Anal. – reference: G. Kunert, A a posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes, Ph.D. Thesis, 1999. – reference: F. Bernis, Viscous flows, fourth order nonlinear degenerate parabolic equations and singular elliptic problems, in free boundary problems: theory and applications, in: Pitman Research Notes in Mathematics, vol. 323, 1995, pp. 40–56. – volume: vol. 1 start-page: 393 year: 1998 end-page: 397 ident: bib70 article-title: Adaptive methods for the numerical solution of the compressible navier-stokes equations publication-title: Computational Fluid Dynamics’98 – start-page: 3 year: 1983 end-page: 17 ident: bib5 article-title: Refinement algorithms and data structures for regular local mesh refinement publication-title: Scientific Computing – volume: 8 start-page: 1356 year: 1996 end-page: 1370 ident: bib1 article-title: Stable and unstable singularities in the unforced hele-shaw cell publication-title: Phys. Fluids – volume: 47 start-page: 4169 year: 1993 end-page: 4181 ident: bib29 article-title: Droplet breakup in a model of the Hele–Shaw cell publication-title: Phys. Rev. E – volume: 129 start-page: 175 year: 1995 end-page: 200 ident: bib11 article-title: Nonnegative solutions of a fourth order nonlinear degenerate parabolic equation publication-title: Arch. Rational Mech. Anal. – volume: 12 start-page: 755 year: 1991 end-page: 786 ident: bib30 article-title: Optimal triangular mesh generation by coordinate transforma tion publication-title: SIAM J. Sci. Stat. Comp. – volume: 12 start-page: 293 year: 2001 end-page: 320 ident: bib47 article-title: Simulation of singularities and instabilities arising in thin film flow publication-title: Eur. Appl. Math. – volume: 32 start-page: 709 year: 1991 end-page: 749 ident: bib65 article-title: Automatic three-dimensional mesh generation by the finite octree technique publication-title: Internat. J. Numer. Method Eng. – volume: 80 start-page: 525 year: 1998 end-page: 556 ident: bib9 article-title: Finite element approximation of a fourth order degenerate parabolic equation publication-title: Numer. Math. – reference: L.A. Freitag, M.T. Jones, P.E. Plassmann, An efficient parallel algorithm for mesh smoothing, in: Proceedings of the 4th International Meshing Roundtables, Sandia Labs, 1995, pp. 47–58. – start-page: 161 year: 1977 end-page: 194 ident: bib57 article-title: Software for C publication-title: Mathematical Software III – reference: W.G. Habashi, M. Fortin, J. Dompierre, M. Vallet, D. Ati-Ali-Yahia, Y. Bourgault, M.P. Robichaud, A. Tam, S. Boivin, Anisotropic mesh optimization for structured and unstructured meshes, in: Proceedings of the 28th Computational Fluid Dynamics Lecture Series, von Karman Institute, March 1997. – reference: L. Chen, P. Sun, J. Xu, Multilevel homotopic adaptive finite element methods for convection dominated problems, in: Domain Decomposition Methods in Science and Engineering, Lecture Notes in Computational Science and Engineering 40 (2004) 459–468. – volume: 84 start-page: 125 year: 1978 end-page: 143 ident: bib45 article-title: On the motion of a small viscous droplet that wets a surface publication-title: J. Fluid Mech. – volume: 17 start-page: S291 year: 2005 end-page: S307 ident: bib10 article-title: The thin film equation: recent advances and some new perspectives publication-title: J. Phys. Condens. Mat. – volume: 83 start-page: 179 year: 1990 end-page: 206 ident: bib13 article-title: Higher order nonlinear degenerate parabolic equations publication-title: J. Differ. Equat. – volume: vol. 363 start-page: 12 year: 1974 end-page: 20 ident: bib33 article-title: Good approximation by splines with variables knots II publication-title: Proceedings of the 11th International Conference on Numerical Methods in Fluid Dynamics, of Lecture Notes in Mathematics – volume: 41 start-page: 2313 year: 2003 end-page: 2332 ident: bib8 article-title: Asymptotically exact a posteriori error estimators, part II: general unstructured grids publication-title: SIAM J. Numer. Anal. – volume: 27 start-page: 401 year: 1996 end-page: 423 ident: bib39 article-title: On the Cahn–Hilliard equation with degenerate mobility publication-title: SIAM J. Math. Anal. – year: 1995 ident: bib25 article-title: High Accuracy Theory of Finite Element Methods – year: 1995 ident: bib72 article-title: Superconvergence in Galkerkin Finite Element Methods – volume: 6 start-page: 1491 year: 1994 end-page: 1504 ident: bib43 article-title: An experimental study of rivulet instabilities in centrifugal spin coating of viscous newtonian and non-newtonian fluids publication-title: Phys. Fluids – volume: 15 start-page: 151 year: 1999 end-page: 167 ident: bib59 article-title: Analysis of a class of superconvergence patch recovery techniques for linear and bilinear finite elements publication-title: Numer. Method PDEs – volume: 109 start-page: 242 year: 1997 end-page: 256 ident: bib40 article-title: Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix publication-title: Physica D – volume: 10 start-page: 297 year: 1999 end-page: 318 ident: bib61 article-title: Numerical and asymptotic results on the linear stability of a thin film spreading down a slope of small inclination publication-title: Eur. J. Appl. Math. – volume: 12 start-page: 253 year: 2001 end-page: 291 ident: bib15 article-title: Stability of compressive and undercompressive thin film travelling waves publication-title: Eur. J. Appl. Math. – volume: 2 start-page: 40 year: 1990 end-page: 72 ident: bib55 article-title: On adaptive grid refinement in the presence of internal or boundary layers publication-title: IMPACT Comput. Sci. Eng. – volume: 4 start-page: 709 year: 1988 end-page: 712 ident: bib41 article-title: Laplacian smoothing and delaunay triangulation publication-title: Commun. Appl. Numer. Method – volume: 73 start-page: 1139 year: 2004 end-page: 1152 ident: bib74 article-title: Analysis of recovery type a posteriori error estimators for mildly structured grids publication-title: Math. Comp. – volume: 7 start-page: 287 year: 1996 end-page: 301 ident: bib22 article-title: The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the laplacian of the mean curvature publication-title: Eur. J. Appl. Math. – volume: 6 start-page: 1063 year: 1989 end-page: 1075 ident: bib31 article-title: On optimal interpolation triangle incidences publication-title: SIAM J. Sci. Stat. Comp. – volume: 174 start-page: 903 year: 2001 ident: 10.1016/j.jcp.2006.11.005_bib49 article-title: Variational mesh adaptation: isotropy and equidistribution publication-title: J. Comput. Phys. doi: 10.1006/jcph.2001.6945 – year: 1995 ident: 10.1016/j.jcp.2006.11.005_bib25 – ident: 10.1016/j.jcp.2006.11.005_bib56 – volume: 8 start-page: 460 year: 1996 ident: 10.1016/j.jcp.2006.11.005_bib67 article-title: Stability of newtonian and viscoelastic dynamic contact line publication-title: Phys. Fluids doi: 10.1063/1.868800 – year: 1996 ident: 10.1016/j.jcp.2006.11.005_bib71 – volume: 34 start-page: 979 year: 1997 ident: 10.1016/j.jcp.2006.11.005_bib6 article-title: Mesh smoothing using a posteriori error estimates publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142994265292 – volume: vol. 606 year: 1977 ident: 10.1016/j.jcp.2006.11.005_bib63 article-title: A mixed finite element method for 2nd order elliptic problems – volume: 76 start-page: 179 year: 2007 ident: 10.1016/j.jcp.2006.11.005_bib28 article-title: Optimal anisotropic simplicial meshes for minimizing interpolation errors in Lp-norm publication-title: Math. Comp. doi: 10.1090/S0025-5718-06-01896-5 – volume: 27 start-page: 401 year: 1996 ident: 10.1016/j.jcp.2006.11.005_bib39 article-title: On the Cahn–Hilliard equation with degenerate mobility publication-title: SIAM J. Math. Anal. doi: 10.1137/S0036141094267662 – volume: 73 start-page: 1139 year: 2004 ident: 10.1016/j.jcp.2006.11.005_bib74 article-title: Analysis of recovery type a posteriori error estimators for mildly structured grids publication-title: Math. Comp. doi: 10.1090/S0025-5718-03-01600-4 – volume: 109 start-page: 242 year: 1997 ident: 10.1016/j.jcp.2006.11.005_bib40 article-title: Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix publication-title: Physica D doi: 10.1016/S0167-2789(97)00066-3 – volume: 346 start-page: 824 year: 1990 ident: 10.1016/j.jcp.2006.11.005_bib24 article-title: Finger instability of this spreading films driven by temperature gradients publication-title: Nature doi: 10.1038/346824a0 – ident: 10.1016/j.jcp.2006.11.005_bib76 – volume: 49 start-page: 85 year: 1996 ident: 10.1016/j.jcp.2006.11.005_bib16 article-title: The lubrication approximation for thin viscous films: regularity and long time behaviour of weak solutions publication-title: Commun. Pure Appl. Math. doi: 10.1002/(SICI)1097-0312(199602)49:2<85::AID-CPA1>3.0.CO;2-2 – volume: 47 start-page: 4169 year: 1993 ident: 10.1016/j.jcp.2006.11.005_bib29 article-title: Droplet breakup in a model of the Hele–Shaw cell publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.47.4169 – volume: 80 start-page: 525 year: 1998 ident: 10.1016/j.jcp.2006.11.005_bib9 article-title: Finite element approximation of a fourth order degenerate parabolic equation publication-title: Numer. Math. doi: 10.1007/s002110050377 – volume: V start-page: 499 year: 1986 ident: 10.1016/j.jcp.2006.11.005_bib62 article-title: Piecewise linear best L2 approximation on triangulations publication-title: Approx. Theory – volume: 300 start-page: 427 year: 1982 ident: 10.1016/j.jcp.2006.11.005_bib51 article-title: Flow and instability of a viscous current down a slope publication-title: Nature doi: 10.1038/300427a0 – volume: vol. 100 year: 1994 ident: 10.1016/j.jcp.2006.11.005_bib19 article-title: Singularities and similarities in interface flow – volume: 69 start-page: 141 year: 1999 ident: 10.1016/j.jcp.2006.11.005_bib75 article-title: Ultraconvergence of the patch recovery technique II publication-title: Math. Comp. doi: 10.1090/S0025-5718-99-01205-3 – volume: 1 start-page: 165 year: 1998 ident: 10.1016/j.jcp.2006.11.005_bib37 article-title: Anisotropic mesh adaptation for finite volume and finite element methods on triangular meshes publication-title: Comput. Visual. Sci. doi: 10.1007/s007910050015 – volume: 62 start-page: 1496 year: 1989 ident: 10.1016/j.jcp.2006.11.005_bib69 article-title: Fingering instability in thin wetting films publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.62.1496 – volume: 12 start-page: 755 year: 1991 ident: 10.1016/j.jcp.2006.11.005_bib32 article-title: Optimal triangular mesh generation by coordinate transformation publication-title: SIAM J. Sci. Stat. Comp. doi: 10.1137/0912040 – ident: 10.1016/j.jcp.2006.11.005_bib44 doi: 10.2172/414390 – volume: vol. 1 start-page: 393 year: 1998 ident: 10.1016/j.jcp.2006.11.005_bib70 article-title: Adaptive methods for the numerical solution of the compressible navier-stokes equations – volume: 33 start-page: 1331 year: 1992 ident: 10.1016/j.jcp.2006.11.005_bib79 article-title: The superconvergence patch recovery and a posteriori error estimates. part 1: the recovery techniques publication-title: Internat. J. Numer. Method Eng. doi: 10.1002/nme.1620330702 – volume: 12 start-page: 253 year: 2001 ident: 10.1016/j.jcp.2006.11.005_bib15 article-title: Stability of compressive and undercompressive thin film travelling waves publication-title: Eur. J. Appl. Math. doi: 10.1017/S0956792501004466 – volume: 184 start-page: 619 year: 2003 ident: 10.1016/j.jcp.2006.11.005_bib50 article-title: Variational mesh adaptation II: error estimates and monitor functions publication-title: J. Comput. Phys. doi: 10.1016/S0021-9991(02)00040-2 – volume: 15 start-page: 736 year: 1978 ident: 10.1016/j.jcp.2006.11.005_bib3 article-title: Error estimates for adaptive finite element computations publication-title: SIAM J. Numer. Anal. doi: 10.1137/0715049 – volume: 12 start-page: 293 year: 2001 ident: 10.1016/j.jcp.2006.11.005_bib47 article-title: Simulation of singularities and instabilities arising in thin film flow publication-title: Eur. Appl. Math. doi: 10.1017/S0956792501004429 – volume: 63 start-page: 011208-1 year: 2000 ident: 10.1016/j.jcp.2006.11.005_bib36 article-title: Global models for moving contact lines publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.63.011208 – volume: 6 start-page: 1491 year: 1994 ident: 10.1016/j.jcp.2006.11.005_bib43 article-title: An experimental study of rivulet instabilities in centrifugal spin coating of viscous newtonian and non-newtonian fluids publication-title: Phys. Fluids doi: 10.1063/1.868263 – volume: 32 start-page: 709 year: 1991 ident: 10.1016/j.jcp.2006.11.005_bib65 article-title: Automatic three-dimensional mesh generation by the finite octree technique publication-title: Internat. J. Numer. Method Eng. doi: 10.1002/nme.1620320406 – volume: 44 start-page: 631 year: 2002 ident: 10.1016/j.jcp.2006.11.005_bib60 article-title: Convergence of adaptive finite element methods publication-title: SIAM Rev. doi: 10.1137/S0036144502409093 – volume: vol. 3 start-page: 197 year: 1996 ident: 10.1016/j.jcp.2006.11.005_bib20 article-title: Anisotropic adaptive mesh generation in two dimensions for cfd – volume: 89 start-page: 641 issue: 4 year: 2001 ident: 10.1016/j.jcp.2006.11.005_bib42 article-title: New anisotropic a priori error estimates publication-title: Numer. Math. doi: 10.1007/s002110100273 – volume: 9 start-page: 530 year: 1997 ident: 10.1016/j.jcp.2006.11.005_bib18 article-title: Linear stability and transient growth in driven contact lines publication-title: Phys. Fluids doi: 10.1063/1.869217 – ident: 10.1016/j.jcp.2006.11.005_bib77 – volume: 6 start-page: 1063 year: 1989 ident: 10.1016/j.jcp.2006.11.005_bib31 article-title: On optimal interpolation triangle incidences publication-title: SIAM J. Sci. Stat. Comp. doi: 10.1137/0910064 – volume: 4 start-page: 234 year: 1992 ident: 10.1016/j.jcp.2006.11.005_bib52 article-title: Finger instability of a gravitationally driven contact line publication-title: Phys. Fluids A doi: 10.1063/1.858351 – start-page: 3 year: 1983 ident: 10.1016/j.jcp.2006.11.005_bib5 article-title: Refinement algorithms and data structures for regular local mesh refinement – volume: 41 start-page: 2313 year: 2003 ident: 10.1016/j.jcp.2006.11.005_bib8 article-title: Asymptotically exact a posteriori error estimators, part II: general unstructured grids publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142901398751 – volume: 10 start-page: 25 year: 1989 ident: 10.1016/j.jcp.2006.11.005_bib68 article-title: Fingering instabilities of driven spreading films publication-title: Europhys. Lett. doi: 10.1209/0295-5075/10/1/005 – volume: 45 start-page: 331 year: 2003 ident: 10.1016/j.jcp.2006.11.005_bib73 article-title: ADI schemes for higher-order nonlinear diffusion equations publication-title: Appl. Numer. Math. doi: 10.1016/S0168-9274(02)00194-0 – volume: 41 start-page: 2294 year: 2003 ident: 10.1016/j.jcp.2006.11.005_bib7 article-title: Asymptotically exact a posteriori error estimators, part I: grids with superconvergence publication-title: SIAM J. Numer. Anal. doi: 10.1137/S003614290139874X – volume: 12 start-page: 755 year: 1991 ident: 10.1016/j.jcp.2006.11.005_bib30 article-title: Optimal triangular mesh generation by coordinate transforma tion publication-title: SIAM J. Sci. Stat. Comp. doi: 10.1137/0912040 – ident: 10.1016/j.jcp.2006.11.005_bib48 – start-page: 161 year: 1977 ident: 10.1016/j.jcp.2006.11.005_bib57 article-title: Software for C1 surface interpolation – volume: 4 start-page: 709 year: 1988 ident: 10.1016/j.jcp.2006.11.005_bib41 article-title: Laplacian smoothing and delaunay triangulation publication-title: Commun. Appl. Numer. Method doi: 10.1002/cnm.1630040603 – volume: 33 start-page: 1365 year: 1992 ident: 10.1016/j.jcp.2006.11.005_bib80 article-title: The superconvergence patch recovery and a posteriori error estimates. part 2: error estimates and adaptivity publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.1620330703 – ident: 10.1016/j.jcp.2006.11.005_bib2 – volume: 3 start-page: 309 year: 1974 ident: 10.1016/j.jcp.2006.11.005_bib21 article-title: Splines (with optimal knots) are better publication-title: Appl. Anal. doi: 10.1080/00036817408839073 – year: 2001 ident: 10.1016/j.jcp.2006.11.005_bib4 article-title: The finite element method and its reliability – volume: 33 start-page: 1106 year: 1996 ident: 10.1016/j.jcp.2006.11.005_bib38 article-title: A convergent adaptive algorithm for poissons equation publication-title: SIAM J. Numer. Anal. doi: 10.1137/0733054 – volume: 14 start-page: 541 year: 1995 ident: 10.1016/j.jcp.2006.11.005_bib46 article-title: Degenerate parabolic differential equations of fourth order and a plasticity model with nonlocal hardening publication-title: Z. Anal. Anwend. doi: 10.4171/ZAA/639 – volume: 129 start-page: 175 year: 1995 ident: 10.1016/j.jcp.2006.11.005_bib11 article-title: Nonnegative solutions of a fourth order nonlinear degenerate parabolic equation publication-title: Arch. Rational Mech. Anal. doi: 10.1007/BF00379920 – volume: 2 start-page: 40 year: 1990 ident: 10.1016/j.jcp.2006.11.005_bib55 article-title: On adaptive grid refinement in the presence of internal or boundary layers publication-title: IMPACT Comput. Sci. Eng. doi: 10.1016/0899-8248(90)90003-S – volume: 7 start-page: 287 year: 1996 ident: 10.1016/j.jcp.2006.11.005_bib22 article-title: The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the laplacian of the mean curvature publication-title: Eur. J. Appl. Math. doi: 10.1017/S0956792500002369 – volume: vol. 21 year: 1973 ident: 10.1016/j.jcp.2006.11.005_bib34 – year: 1995 ident: 10.1016/j.jcp.2006.11.005_bib72 – volume: 183 start-page: 274 year: 2002 ident: 10.1016/j.jcp.2006.11.005_bib35 article-title: Computing three-dimensional thin film flows including contact lines publication-title: J. Comp. Phys. doi: 10.1006/jcph.2002.7197 – ident: 10.1016/j.jcp.2006.11.005_bib26 – volume: 15 start-page: 151 year: 1999 ident: 10.1016/j.jcp.2006.11.005_bib59 article-title: Analysis of a class of superconvergence patch recovery techniques for linear and bilinear finite elements publication-title: Numer. Method PDEs doi: 10.1002/(SICI)1098-2426(199903)15:2<151::AID-NUM2>3.0.CO;2-O – volume: 28 start-page: 5 year: 1985 ident: 10.1016/j.jcp.2006.11.005_bib66 article-title: On the rewetting of an inclined solid surface by a liquid publication-title: Phys. Fluids doi: 10.1063/1.865410 – volume: 45 start-page: 277 year: 1994 ident: 10.1016/j.jcp.2006.11.005_bib58 article-title: Spatial coupling of plant and herbivore dynamics: the contribution of herbivore dispersal to transient and persistent waves of damage publication-title: Theor. Popul. Biol. doi: 10.1006/tpbi.1994.1014 – volume: 17 start-page: S291 year: 2005 ident: 10.1016/j.jcp.2006.11.005_bib10 article-title: The thin film equation: recent advances and some new perspectives publication-title: J. Phys. Condens. Mat. doi: 10.1088/0953-8984/17/9/002 – volume: 84 start-page: 125 year: 1978 ident: 10.1016/j.jcp.2006.11.005_bib45 article-title: On the motion of a small viscous droplet that wets a surface publication-title: J. Fluid Mech. doi: 10.1017/S0022112078000075 – volume: 56 start-page: 681 year: 1996 ident: 10.1016/j.jcp.2006.11.005_bib17 article-title: Symmetric singularity formation in lubrication-type equations for interface motion publication-title: SIAM J. Appl. Math. doi: 10.1137/S0036139994271972 – volume: 248 year: 1990 ident: 10.1016/j.jcp.2006.11.005_bib23 article-title: On the origin of the bump in the profile of surface-tension-gradient-driven spreading films publication-title: Mat. Res. Soc. Symp. Proc. – volume: 45 start-page: 95 year: 2003 ident: 10.1016/j.jcp.2006.11.005_bib53 article-title: Instabilities in gravity driven flow of thin fluid publication-title: SIAM Rev. doi: 10.1137/S003614450240135 – volume: vol. 363 start-page: 12 year: 1974 ident: 10.1016/j.jcp.2006.11.005_bib33 article-title: Good approximation by splines with variables knots II – volume: 37 start-page: 523 year: 2000 ident: 10.1016/j.jcp.2006.11.005_bib78 article-title: Positivity preserving numerical schemes for lubrication-type equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142998335698 – volume: 13 start-page: 3168 year: 2001 ident: 10.1016/j.jcp.2006.11.005_bib54 article-title: Pattern formation in the flow of thin films down an incline:constant flux configuration publication-title: Phys. Fluids doi: 10.1063/1.1409965 – volume: 83 start-page: 179 year: 1990 ident: 10.1016/j.jcp.2006.11.005_bib13 article-title: Higher order nonlinear degenerate parabolic equations publication-title: J. Differ. Equat. doi: 10.1016/0022-0396(90)90074-Y – volume: vol. 323 year: 1995 ident: 10.1016/j.jcp.2006.11.005_bib14 article-title: Loss and gain of regularity in a lubrication equation for thin viscous films, in Free boundary problems: theory and applications – ident: 10.1016/j.jcp.2006.11.005_bib27 doi: 10.1007/3-540-26825-1_47 – volume: 8 start-page: 1356 year: 1996 ident: 10.1016/j.jcp.2006.11.005_bib1 article-title: Stable and unstable singularities in the unforced hele-shaw cell publication-title: Phys. Fluids doi: 10.1063/1.868915 – ident: 10.1016/j.jcp.2006.11.005_bib12 – volume: 21 start-page: 604 year: 1984 ident: 10.1016/j.jcp.2006.11.005_bib64 article-title: Mesh refinement processes based on the generalized bisection of simplices publication-title: SIAM J. Numer. Anal. doi: 10.1137/0721042 – volume: 10 start-page: 297 year: 1999 ident: 10.1016/j.jcp.2006.11.005_bib61 article-title: Numerical and asymptotic results on the linear stability of a thin film spreading down a slope of small inclination publication-title: Eur. J. Appl. Math. doi: 10.1017/S0956792599003769 |
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| Snippet | A new adaptive local mesh refinement method is presented for thin film flow problems containing moving contact lines. Based on adaptation on an optimal... |
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| SubjectTerms | Adaptive mesh Computational techniques Exact sciences and technology Local refinement Mathematical methods in physics Mixed finite element method Moving contact lines Physics Thin film flow |
| Title | A new adaptive local mesh refinement algorithm and its application on fourth order thin film flow problem |
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