A second-order face-centred finite volume method for elliptic problems
A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). The method is based on a mixed formulation and...
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| Veröffentlicht in: | Computer methods in applied mechanics and engineering Jg. 358; S. 112655 |
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01.01.2020
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| Abstract | A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). The method is based on a mixed formulation and therefore considers the solution and its gradient as independent unknowns. They are computed solving a cell-by-cell problem after the solution at the faces is determined. The proposed approach avoids the need of reconstructing the solution gradient, as required by cell-centred and vertex-centred FV methods. This strategy leads to a method that is insensitive to mesh distortion and stretching. The current method is second-order and requires the solution of a global system of equations of identical size and identical number of non-zero elements when compared to the recently proposed first-order FCFV. The formulation is presented for Poisson and Stokes problems. Numerical examples are used to illustrate the approximation properties of the method as well as to demonstrate its potential in three dimensional problems with complex geometries. The integration of a mesh adaptive procedure in the FCFV solution algorithm is also presented.
•New accurate and efficient second-order face-centred finite volume method (FCFV).•Second-order convergence of the solution and first-order convergence of its gradient.•No flux reconstruction needed and robustness to cell distortion and stretching.•Application to Poisson and incompressible Stokes problems in 2D and 3D.•Automatic mesh adaptivity driven by an error indicator from 1st and 2nd order FCFVs. |
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| AbstractList | A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). The method is based on a mixed formulation and therefore considers the solution and its gradient as independent unknowns. They are computed solving a cell-by-cell problem after the solution at the faces is determined. The proposed approach avoids the need of reconstructing the solution gradient, as required by cell-centred and vertex-centred FV methods. This strategy leads to a method that is insensitive to mesh distortion and stretching. The current method is second-order and requires the solution of a global system of equations of identical size and identical number of non-zero elements when compared to the recently proposed first-order FCFV. The formulation is presented for Poisson and Stokes problems. Numerical examples are used to illustrate the approximation properties of the method as well as to demonstrate its potential in three dimensional problems with complex geometries. The integration of a mesh adaptive procedure in the FCFV solution algorithm is also presented.
•New accurate and efficient second-order face-centred finite volume method (FCFV).•Second-order convergence of the solution and first-order convergence of its gradient.•No flux reconstruction needed and robustness to cell distortion and stretching.•Application to Poisson and incompressible Stokes problems in 2D and 3D.•Automatic mesh adaptivity driven by an error indicator from 1st and 2nd order FCFVs. A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). The method is based on a mixed formulation and therefore considers the solution and its gradient as independent unknowns. They are computed solving a cell-by-cell problem after the solution at the faces is determined. The proposed approach avoids the need of reconstructing the solution gradient, as required by cell-centred and vertex-centred FV methods. This strategy leads to a method that is insensitive to mesh distortion and stretching. The current method is second-order and requires the solution of a global system of equations of identical size and identical number of non-zero elements when compared to the recently proposed first-order FCFV. The formulation is presented for Poisson and Stokes problems. Numerical examples are used to illustrate the approximation properties of the method as well as to demonstrate its potential in three dimensional problems with complex geometries. The integration of a mesh adaptive procedure in the FCFV solution algorithm is also presented. |
| ArticleNumber | 112655 |
| Author | Vieira, Luan M. Giacomini, Matteo Sevilla, Ruben Huerta, Antonio |
| Author_xml | – sequence: 1 givenname: Luan M. surname: Vieira fullname: Vieira, Luan M. organization: Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Bay Campus, SA1 8EN, Wales, United Kingdom – sequence: 2 givenname: Matteo orcidid: 0000-0001-6094-5944 surname: Giacomini fullname: Giacomini, Matteo organization: Laboratori de Calcul Numeric (LaCàN), ETS de Ingenieros de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya Barcelona, Spain – sequence: 3 givenname: Ruben orcidid: 0000-0002-0061-6214 surname: Sevilla fullname: Sevilla, Ruben email: r.sevilla@swansea.ac.uk organization: Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Bay Campus, SA1 8EN, Wales, United Kingdom – sequence: 4 givenname: Antonio orcidid: 0000-0003-4198-3798 surname: Huerta fullname: Huerta, Antonio organization: Laboratori de Calcul Numeric (LaCàN), ETS de Ingenieros de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya Barcelona, Spain |
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| Cites_doi | 10.1093/imanum/drv067 10.1007/s10915-010-9359-0 10.1137/070706616 10.1007/s10915-014-9962-6 10.1016/j.jcp.2009.01.030 10.1016/j.compstruc.2019.05.005 10.2514/1.44940 10.1002/nme.5833 10.1007/s10915-018-0855-y 10.1007/s10915-015-0090-8 10.2514/1.J050897 10.1016/j.cma.2009.10.007 10.1002/fld.1716 10.1073/pnas.1707815114 10.1137/04061060X 10.1002/gamm.201490017 10.1007/s10915-018-0657-2 10.1016/j.jcp.2010.10.032 10.1016/j.cma.2012.08.016 10.1016/S0045-7825(98)00338-7 10.1142/S0218202514400041 10.1016/j.jcp.2015.07.029 10.1090/S0025-5718-08-02123-6 10.1016/j.jcp.2009.08.030 10.1016/j.compstruc.2018.10.015 10.1017/S0962492906300013 10.1137/S0036142902417893 10.1002/nme.5916 |
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| References | Sevilla (b31) 2019; 220 Oikawa (b16) 2015; 65 Nguyen, Peraire, Cockburn (b21) 2009; 228 Nguyen, Peraire, Cockburn (b26) 2011; 230 Yang, Liu, Li, Marchesoni, Hänggi, Zhang (b34) 2017; 114 Cockburn, Gopalakrishnan (b14) 2005; 28 Morton, Sonar (b3) 2007; 16 Díez, Huerta (b33) 1999; 176 Aguirre, Gil, Bonet, Lee (b10) 2015; 300 Cockburn, Gopalakrishnan (b12) 2004; 42 Cockburn, Dong, Guzmán (b24) 2008; 77 Droniou (b6) 2014; 24 Donea, Huerta (b28) 2003 Montlaur, Fernández-Méndez, Huerta (b20) 2008; 57 Sevilla, Giacomini, Karkoulias, Huerta (b30) 2018; 116 Nguyen, Peraire, Cockburn (b25) 2009; 228 Eymard, Gallouët, Herbin (b5) 2000; 7 Chassaing, Nogueira, Khelladi (b9) 2013; 253 Cockburn, Gopalakrishnan, Lazarov (b15) 2009; 47 Qiu, Shi (b18) 2016; 36 LeVeque (b1) 2002 Barth, Ohlberger (b4) 2004 Cockburn, Gopalakrishnan (b13) 2005; 43 Sevilla, Giacomini, Huerta (b19) 2019; 212 Diskin, Thomas (b8) 2011; 49 Sevilla, Huerta (b23) 2016; vol. 566 Oikawa (b17) 2016; 67 Diskin, Thomas, Nielsen, Nishikawa, White (b7) 2010; 48 Sevilla, Huerta (b27) 2018; 77 Toro (b2) 2009 Cockburn, Nguyen, Peraire (b32) 2010; 45 Giacomini, Karkoulias, Sevilla, Huerta (b29) 2018; 77 Sevilla, Giacomini, Huerta (b11) 2018; 115 Nguyen, Peraire, Cockburn (b22) 2010; 199 Barth (10.1016/j.cma.2019.112655_b4) 2004 Nguyen (10.1016/j.cma.2019.112655_b22) 2010; 199 Díez (10.1016/j.cma.2019.112655_b33) 1999; 176 Sevilla (10.1016/j.cma.2019.112655_b23) 2016; vol. 566 Yang (10.1016/j.cma.2019.112655_b34) 2017; 114 Montlaur (10.1016/j.cma.2019.112655_b20) 2008; 57 Sevilla (10.1016/j.cma.2019.112655_b31) 2019; 220 Oikawa (10.1016/j.cma.2019.112655_b17) 2016; 67 Chassaing (10.1016/j.cma.2019.112655_b9) 2013; 253 Donea (10.1016/j.cma.2019.112655_b28) 2003 Morton (10.1016/j.cma.2019.112655_b3) 2007; 16 Giacomini (10.1016/j.cma.2019.112655_b29) 2018; 77 Cockburn (10.1016/j.cma.2019.112655_b14) 2005; 28 Sevilla (10.1016/j.cma.2019.112655_b27) 2018; 77 Droniou (10.1016/j.cma.2019.112655_b6) 2014; 24 Qiu (10.1016/j.cma.2019.112655_b18) 2016; 36 Sevilla (10.1016/j.cma.2019.112655_b30) 2018; 116 Cockburn (10.1016/j.cma.2019.112655_b13) 2005; 43 Toro (10.1016/j.cma.2019.112655_b2) 2009 Sevilla (10.1016/j.cma.2019.112655_b19) 2019; 212 Nguyen (10.1016/j.cma.2019.112655_b26) 2011; 230 Nguyen (10.1016/j.cma.2019.112655_b25) 2009; 228 LeVeque (10.1016/j.cma.2019.112655_b1) 2002 Cockburn (10.1016/j.cma.2019.112655_b32) 2010; 45 Cockburn (10.1016/j.cma.2019.112655_b24) 2008; 77 Diskin (10.1016/j.cma.2019.112655_b8) 2011; 49 Sevilla (10.1016/j.cma.2019.112655_b11) 2018; 115 Oikawa (10.1016/j.cma.2019.112655_b16) 2015; 65 Diskin (10.1016/j.cma.2019.112655_b7) 2010; 48 Aguirre (10.1016/j.cma.2019.112655_b10) 2015; 300 Nguyen (10.1016/j.cma.2019.112655_b21) 2009; 228 Cockburn (10.1016/j.cma.2019.112655_b12) 2004; 42 Eymard (10.1016/j.cma.2019.112655_b5) 2000; 7 Cockburn (10.1016/j.cma.2019.112655_b15) 2009; 47 |
| References_xml | – volume: 116 start-page: 91 year: 2018 end-page: 116 ident: b30 article-title: A superconvergent hybridisable discontinuous Galerkin method for linear elasticity publication-title: Internat. J. Numer. Methods Engrg. – year: 2009 ident: b2 article-title: Riemann Solvers and Numerical Methods for Fluid Dynamics – volume: 57 start-page: 1071 year: 2008 end-page: 1092 ident: b20 article-title: Discontinuous Galerkin methods for the Stokes equations using divergence-free approximations publication-title: Internat. J. Numer. Methods Fluids – volume: 48 start-page: 1326 year: 2010 ident: b7 article-title: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: viscous fluxes publication-title: AIAA J. – volume: 228 start-page: 3232 year: 2009 end-page: 3254 ident: b21 article-title: An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations publication-title: J. Comput. Phys. – volume: 77 start-page: 1679 year: 2018 end-page: 1702 ident: b29 article-title: A superconvergent HDG method for Stokes flow with strongly enforced symmetry of the stress tensor publication-title: J. Sci. Comput. – volume: 43 start-page: 1627 year: 2005 end-page: 1650 ident: b13 article-title: Incompressible finite elements via hybridization. I. The Stokes system in two space dimensions publication-title: SIAM J. Numer. Anal. – volume: 114 start-page: 9564 year: 2017 end-page: 9569 ident: b34 article-title: Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels publication-title: Proc. Natl. Acad. Sci. – volume: 65 start-page: 327 year: 2015 end-page: 340 ident: b16 article-title: A hybridized discontinuous Galerkin method with reduced stabilization publication-title: J. Sci. Comput. – volume: 16 start-page: 155 year: 2007 end-page: 238 ident: b3 article-title: Finite volume methods for hyperbolic conservation laws publication-title: Acta Numer. – volume: 253 start-page: 463 year: 2013 end-page: 478 ident: b9 article-title: Moving kriging reconstruction for high-order finite volume computation of compressible flows publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 67 start-page: 475 year: 2016 end-page: 492 ident: b17 article-title: Analysis of a reduced-order HDG method for the Stokes equations publication-title: J. Sci. Comput. – volume: 228 start-page: 8841 year: 2009 end-page: 8855 ident: b25 article-title: An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations publication-title: J. Comput. Phys. – volume: vol. 566 start-page: 105 year: 2016 end-page: 129 ident: b23 article-title: Tutorial on Hybridizable Discontinuous Galerkin (HDG) for second-order elliptic problems publication-title: Advanced Finite Element Technologies – volume: 42 start-page: 283 year: 2004 end-page: 301 ident: b12 article-title: A characterization of hybridized mixed methods for second order elliptic problems publication-title: SIAM J. Numer. Anal. – volume: 300 start-page: 387 year: 2015 end-page: 422 ident: b10 article-title: An upwind vertex centred finite volume solver for Lagrangian solid dynamics publication-title: J. Comput. Phys. – volume: 49 start-page: 836 year: 2011 end-page: 854 ident: b8 article-title: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes publication-title: AIAA J. – volume: 176 start-page: 215 year: 1999 end-page: 229 ident: b33 article-title: A unified approach to remeshing strategies for finite element publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 115 start-page: 986 year: 2018 end-page: 1014 ident: b11 article-title: A face-centred finite volume method for second-order elliptic problems publication-title: Internat. J. Numer. Methods Engrg. – volume: 220 start-page: 69 year: 2019 end-page: 80 ident: b31 article-title: HDG-NEFEM for two dimensional linear elasticity publication-title: Comput. Struct. – volume: 28 start-page: 154 year: 2005 end-page: 182 ident: b14 article-title: New hybridization techniques publication-title: GAMM-Mitt. – year: 2002 ident: b1 article-title: Finite Volume Methods for Hyperbolic Problems publication-title: Cambridge Texts in Applied Mathematics – volume: 47 start-page: 1319 year: 2009 end-page: 1365 ident: b15 article-title: Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems publication-title: SIAM J. Numer. Anal. – volume: 36 start-page: 1943 year: 2016 end-page: 1967 ident: b18 article-title: A superconvergent HDG method for the incompressible Navier–Stokes equations on general polyhedral meshes publication-title: IMA J. Numer. Anal. – volume: 212 start-page: 43 year: 2019 end-page: 57 ident: b19 article-title: A locking-free face-centred finite volume (FCFV) method for linear elastostatics publication-title: Comput. Struct. – year: 2004 ident: b4 article-title: Finite volume methods: Foundation and analysis publication-title: Encyclopedia of Computational Mechanics – volume: 77 start-page: 1953 year: 2018 end-page: 1980 ident: b27 article-title: HDG-NEFEM with degree adaptivity for Stokes flows publication-title: J. Sci. Comput. – volume: 230 start-page: 1147 year: 2011 end-page: 1170 ident: b26 article-title: An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations publication-title: J. Comput. Phys. – volume: 7 start-page: 713 year: 2000 end-page: 1018 ident: b5 article-title: Finite volume methods publication-title: Handb. Numer. Anal. – volume: 199 start-page: 582 year: 2010 end-page: 597 ident: b22 article-title: A hybridizable discontinuous Galerkin method for Stokes flow publication-title: Comput. Methods Appl. Mech. Engrg. – year: 2003 ident: b28 publication-title: Finite Element Methods for Flow Problems – volume: 45 start-page: 215 year: 2010 end-page: 237 ident: b32 article-title: A comparison of HDG methods for Stokes flow publication-title: J. Sci. Comput. – volume: 24 start-page: 1575 year: 2014 end-page: 1619 ident: b6 article-title: Finite volume schemes for diffusion equations: Introduction to and review of modern methods publication-title: Math. Models Methods Appl. Sci. – volume: 77 start-page: 1887 year: 2008 end-page: 1916 ident: b24 article-title: A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems publication-title: Math. Comp. – volume: 36 start-page: 1943 issue: 4 year: 2016 ident: 10.1016/j.cma.2019.112655_b18 article-title: A superconvergent HDG method for the incompressible Navier–Stokes equations on general polyhedral meshes publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drv067 – volume: 45 start-page: 215 issue: 1–3 year: 2010 ident: 10.1016/j.cma.2019.112655_b32 article-title: A comparison of HDG methods for Stokes flow publication-title: J. Sci. Comput. doi: 10.1007/s10915-010-9359-0 – volume: 47 start-page: 1319 issue: 2 year: 2009 ident: 10.1016/j.cma.2019.112655_b15 article-title: Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems publication-title: SIAM J. Numer. Anal. doi: 10.1137/070706616 – volume: 65 start-page: 327 issue: 1 year: 2015 ident: 10.1016/j.cma.2019.112655_b16 article-title: A hybridized discontinuous Galerkin method with reduced stabilization publication-title: J. Sci. Comput. doi: 10.1007/s10915-014-9962-6 – volume: 228 start-page: 3232 issue: 9 year: 2009 ident: 10.1016/j.cma.2019.112655_b21 article-title: An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2009.01.030 – volume: 220 start-page: 69 year: 2019 ident: 10.1016/j.cma.2019.112655_b31 article-title: HDG-NEFEM for two dimensional linear elasticity publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2019.05.005 – volume: 48 start-page: 1326 issue: 7 year: 2010 ident: 10.1016/j.cma.2019.112655_b7 article-title: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: viscous fluxes publication-title: AIAA J. doi: 10.2514/1.44940 – volume: 115 start-page: 986 issue: 8 year: 2018 ident: 10.1016/j.cma.2019.112655_b11 article-title: A face-centred finite volume method for second-order elliptic problems publication-title: Internat. J. Numer. Methods Engrg. doi: 10.1002/nme.5833 – volume: 77 start-page: 1679 issue: 3 year: 2018 ident: 10.1016/j.cma.2019.112655_b29 article-title: A superconvergent HDG method for Stokes flow with strongly enforced symmetry of the stress tensor publication-title: J. Sci. Comput. doi: 10.1007/s10915-018-0855-y – volume: 67 start-page: 475 issue: 2 year: 2016 ident: 10.1016/j.cma.2019.112655_b17 article-title: Analysis of a reduced-order HDG method for the Stokes equations publication-title: J. Sci. Comput. doi: 10.1007/s10915-015-0090-8 – year: 2002 ident: 10.1016/j.cma.2019.112655_b1 article-title: Finite Volume Methods for Hyperbolic Problems – volume: 49 start-page: 836 issue: 4 year: 2011 ident: 10.1016/j.cma.2019.112655_b8 article-title: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes publication-title: AIAA J. doi: 10.2514/1.J050897 – volume: vol. 566 start-page: 105 year: 2016 ident: 10.1016/j.cma.2019.112655_b23 article-title: Tutorial on Hybridizable Discontinuous Galerkin (HDG) for second-order elliptic problems – volume: 199 start-page: 582 issue: 9–12 year: 2010 ident: 10.1016/j.cma.2019.112655_b22 article-title: A hybridizable discontinuous Galerkin method for Stokes flow publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2009.10.007 – year: 2003 ident: 10.1016/j.cma.2019.112655_b28 – volume: 57 start-page: 1071 issue: 9 year: 2008 ident: 10.1016/j.cma.2019.112655_b20 article-title: Discontinuous Galerkin methods for the Stokes equations using divergence-free approximations publication-title: Internat. J. Numer. Methods Fluids doi: 10.1002/fld.1716 – volume: 114 start-page: 9564 issue: 36 year: 2017 ident: 10.1016/j.cma.2019.112655_b34 article-title: Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.1707815114 – volume: 43 start-page: 1627 issue: 4 year: 2005 ident: 10.1016/j.cma.2019.112655_b13 article-title: Incompressible finite elements via hybridization. I. The Stokes system in two space dimensions publication-title: SIAM J. Numer. Anal. doi: 10.1137/04061060X – volume: 28 start-page: 154 issue: 2 year: 2005 ident: 10.1016/j.cma.2019.112655_b14 article-title: New hybridization techniques publication-title: GAMM-Mitt. doi: 10.1002/gamm.201490017 – year: 2009 ident: 10.1016/j.cma.2019.112655_b2 – volume: 77 start-page: 1953 issue: 3 year: 2018 ident: 10.1016/j.cma.2019.112655_b27 article-title: HDG-NEFEM with degree adaptivity for Stokes flows publication-title: J. Sci. Comput. doi: 10.1007/s10915-018-0657-2 – volume: 230 start-page: 1147 issue: 4 year: 2011 ident: 10.1016/j.cma.2019.112655_b26 article-title: An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2010.10.032 – volume: 253 start-page: 463 year: 2013 ident: 10.1016/j.cma.2019.112655_b9 article-title: Moving kriging reconstruction for high-order finite volume computation of compressible flows publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2012.08.016 – year: 2004 ident: 10.1016/j.cma.2019.112655_b4 article-title: Finite volume methods: Foundation and analysis – volume: 176 start-page: 215 issue: 1–4 year: 1999 ident: 10.1016/j.cma.2019.112655_b33 article-title: A unified approach to remeshing strategies for finite element h-adaptivity publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/S0045-7825(98)00338-7 – volume: 24 start-page: 1575 issue: 08 year: 2014 ident: 10.1016/j.cma.2019.112655_b6 article-title: Finite volume schemes for diffusion equations: Introduction to and review of modern methods publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202514400041 – volume: 7 start-page: 713 year: 2000 ident: 10.1016/j.cma.2019.112655_b5 article-title: Finite volume methods publication-title: Handb. Numer. Anal. – volume: 300 start-page: 387 year: 2015 ident: 10.1016/j.cma.2019.112655_b10 article-title: An upwind vertex centred finite volume solver for Lagrangian solid dynamics publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2015.07.029 – volume: 77 start-page: 1887 issue: 264 year: 2008 ident: 10.1016/j.cma.2019.112655_b24 article-title: A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems publication-title: Math. Comp. doi: 10.1090/S0025-5718-08-02123-6 – volume: 228 start-page: 8841 issue: 23 year: 2009 ident: 10.1016/j.cma.2019.112655_b25 article-title: An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2009.08.030 – volume: 212 start-page: 43 year: 2019 ident: 10.1016/j.cma.2019.112655_b19 article-title: A locking-free face-centred finite volume (FCFV) method for linear elastostatics publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2018.10.015 – volume: 16 start-page: 155 year: 2007 ident: 10.1016/j.cma.2019.112655_b3 article-title: Finite volume methods for hyperbolic conservation laws publication-title: Acta Numer. doi: 10.1017/S0962492906300013 – volume: 42 start-page: 283 issue: 1 year: 2004 ident: 10.1016/j.cma.2019.112655_b12 article-title: A characterization of hybridized mixed methods for second order elliptic problems publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142902417893 – volume: 116 start-page: 91 issue: 2 year: 2018 ident: 10.1016/j.cma.2019.112655_b30 article-title: A superconvergent hybridisable discontinuous Galerkin method for linear elasticity publication-title: Internat. J. Numer. Methods Engrg. doi: 10.1002/nme.5916 |
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| SubjectTerms | Adaptive algorithms Face-centred Finite volume method Hybridisable discontinuous Galerkin Second-order convergence |
| Title | A second-order face-centred finite volume method for elliptic problems |
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