Numerical solution to a stokes interface problem
A numerical algorithm is described for solving the generalized eigenvalue problem arising in the study of the spectrum of a preconditioned operator in the pressure equation derived from a Stokes interface problem. The algorithm is implemented for two finite element schemes. It is tested for a proble...
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| Vydáno v: | Computational mathematics and mathematical physics Ročník 49; číslo 1; s. 105 - 116 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Dordrecht
SP MAIK Nauka/Interperiodica
01.01.2009
Springer Nature B.V |
| Témata: | |
| ISSN: | 0965-5425, 1555-6662 |
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| Abstract | A numerical algorithm is described for solving the generalized eigenvalue problem arising in the study of the spectrum of a preconditioned operator in the pressure equation derived from a Stokes interface problem. The algorithm is implemented for two finite element schemes. It is tested for a problem with an analytical solution and is applied to spectrum computations in the case of a piecewise constant viscosity. A large number of numerical experiments are analyzed, and recommendations are given for solving the Stokes interface problem in practice. |
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| AbstractList | A numerical algorithm is described for solving the generalized eigenvalue problem arising in the study of the spectrum of a preconditioned operator in the pressure equation derived from a Stokes interface problem. The algorithm is implemented for two finite element schemes. It is tested for a problem with an analytical solution and is applied to spectrum computations in the case of a piecewise constant viscosity. A large number of numerical experiments are analyzed, and recommendations are given for solving the Stokes interface problem in practice. A numerical algorithm is described for solving the generalized eigenvalue problem arising in the study of the spectrum of a preconditioned operator in the pressure equation derived from a Stokes interface problem. The algorithm is implemented for two finite element schemes. It is tested for a problem with an analytical solution and is applied to spectrum computations in the case of a piecewise constant viscosity. A large number of numerical experiments are analyzed, and recommendations are given for solving the Stokes interface problem in practice.[PUBLICATION ABSTRACT] |
| Author | Chizhonkov, E. V. |
| Author_xml | – sequence: 1 givenname: E. V. surname: Chizhonkov fullname: Chizhonkov, E. V. email: chizhonk@mech.math.msu.ru organization: Faculty of Mechanics and Mathematics, Moscow State University |
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| Cites_doi | 10.1007/s002110200395 10.1016/0021-9991(92)90240-Y 10.1051/m2an:2000110 10.1007/s00211-005-0646-x 10.1006/jcph.2000.6636 10.1007/s002110050336 10.1016/S1570-8659(05)80042-0 |
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| DOI | 10.1134/S0965542509010084 |
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| Keywords | numerical solution algorithm for the generalized eigenvalue problem finite element method Stokes interface problem |
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| References_xml | – year: 1995 ident: CR15 publication-title: On the Constant in the LBB Condition for Ring Domains – year: 1995 ident: CR11 publication-title: On the Constant in the LBB Condition for Rectangular Domains – volume: 95 start-page: 735 year: 2003 end-page: 759 ident: CR4 article-title: Optimal a Priori Estimates for Interface Problems publication-title: Numer. Math. doi: 10.1007/s002110200395 – volume: 100 start-page: 335 year: 1992 end-page: 354 ident: CR1 article-title: A Continuum Method for Modeling Surface Tension publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(92)90240-Y – volume: 39 start-page: 2019 year: 1999 end-page: 2049 ident: CR5 article-title: Efficient Methods for Stiff Multidimensional Multiparametric Problems publication-title: Zh. Vychisl. Mat. Mat. Fiz. – year: 1962 ident: CR18 publication-title: Numerical Methods for Scientists and Engineers – volume: 34 start-page: 935 year: 2000 end-page: 951 ident: CR13 article-title: On the Domain Geometry Dependence of the LBB Condition publication-title: Math. Model. Numer. Anal. doi: 10.1051/m2an:2000110 – ident: CR14 – volume: 28 start-page: 43 issue: 3171 year: 1973 end-page: 82 ident: CR9 article-title: Spectrum of an Operator Pencil in Elasticity publication-title: Usp. Mat. Nauk – ident: CR12 – ident: CR17 – year: 1978 ident: CR16 publication-title: Methods for Solving Grid Equations – year: 2002 ident: CR6 publication-title: Relaxation Methods for Saddle Problems – volume: 103 start-page: 129 year: 2006 end-page: 149 ident: CR7 article-title: Analysis of a Stokes Interface Problem publication-title: Numer. Math. doi: 10.1007/s00211-005-0646-x – start-page: 242 year: 1997 end-page: 249 ident: CR10 article-title: On an Operator Related to the Convergence of Uzawa’s Algorithm for the Stokes Equation publication-title: Computational Science for 21st Century – volume: 169 start-page: 463 year: 2001 end-page: 502 ident: CR2 article-title: Level Set Methods: An Overview and Some Recent Results publication-title: J. Comput. Phys. doi: 10.1006/jcph.2000.6636 – volume: 79 start-page: 175 year: 1998 end-page: 202 ident: CR3 article-title: Finite Element Method and Its Convergence for Elliptic and Parabolic Interface Problems publication-title: Numer. Math. doi: 10.1007/s002110050336 – year: 1989 ident: CR8 publication-title: Finite Element Methods for Viscous Incompressible Flow: A Guide to Theory, Practice, and Algorithms – ident: 1008_CR12 – volume: 79 start-page: 175 year: 1998 ident: 1008_CR3 publication-title: Numer. Math. doi: 10.1007/s002110050336 – volume-title: Numerical Methods for Scientists and Engineers year: 1962 ident: 1008_CR18 – volume-title: Finite Element Methods for Viscous Incompressible Flow: A Guide to Theory, Practice, and Algorithms year: 1989 ident: 1008_CR8 – volume-title: On the Constant in the LBB Condition for Rectangular Domains year: 1995 ident: 1008_CR11 – volume-title: On the Constant in the LBB Condition for Ring Domains year: 1995 ident: 1008_CR15 – ident: 1008_CR17 – ident: 1008_CR14 doi: 10.1016/S1570-8659(05)80042-0 – volume: 103 start-page: 129 year: 2006 ident: 1008_CR7 publication-title: Numer. Math. doi: 10.1007/s00211-005-0646-x – volume: 28 start-page: 43 issue: 3171 year: 1973 ident: 1008_CR9 publication-title: Usp. Mat. Nauk – volume: 169 start-page: 463 year: 2001 ident: 1008_CR2 publication-title: J. Comput. Phys. doi: 10.1006/jcph.2000.6636 – start-page: 242 volume-title: Computational Science for 21st Century year: 1997 ident: 1008_CR10 – volume: 95 start-page: 735 year: 2003 ident: 1008_CR4 publication-title: Numer. Math. doi: 10.1007/s002110200395 – volume: 100 start-page: 335 year: 1992 ident: 1008_CR1 publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(92)90240-Y – volume: 39 start-page: 2019 year: 1999 ident: 1008_CR5 publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume-title: Relaxation Methods for Saddle Problems year: 2002 ident: 1008_CR6 – volume-title: Methods for Solving Grid Equations year: 1978 ident: 1008_CR16 – volume: 34 start-page: 935 year: 2000 ident: 1008_CR13 publication-title: Math. Model. Numer. Anal. doi: 10.1051/m2an:2000110 |
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| Title | Numerical solution to a stokes interface problem |
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