Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem
In this paper, we introduce and analyze H(div)-conforming finite element methods for a nonlinear model in poroelasticity. More precisely, the flow variables are discretized by H(div)-conforming mixed finite elements, while the elastic displacement is approximated by the H(div)-conforming finite elem...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/9464389 |
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| _version_ | 1832546903948001280 |
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| author | Yuping Zeng Zhifeng Weng Fen Liang |
| author_facet | Yuping Zeng Zhifeng Weng Fen Liang |
| author_sort | Yuping Zeng |
| collection | DOAJ |
| description | In this paper, we introduce and analyze H(div)-conforming finite element methods for a nonlinear model in poroelasticity. More precisely, the flow variables are discretized by H(div)-conforming mixed finite elements, while the elastic displacement is approximated by the H(div)-conforming finite element with the interior penalty discontinuous Galerkin formulation. Optimal a priori error estimates are derived for both semidiscrete and fully discrete schemes. |
| format | Article |
| id | doaj-art-ccdd0f0cb1414dad96f0623e68af8866 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-ccdd0f0cb1414dad96f0623e68af88662025-02-03T06:46:54ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/94643899464389Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity ProblemYuping Zeng0Zhifeng Weng1Fen Liang2School of Mathematics, Jiaying University, Meizhou 514015, ChinaFujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, ChinaSchool of Mathematics, Jiaying University, Meizhou 514015, ChinaIn this paper, we introduce and analyze H(div)-conforming finite element methods for a nonlinear model in poroelasticity. More precisely, the flow variables are discretized by H(div)-conforming mixed finite elements, while the elastic displacement is approximated by the H(div)-conforming finite element with the interior penalty discontinuous Galerkin formulation. Optimal a priori error estimates are derived for both semidiscrete and fully discrete schemes.http://dx.doi.org/10.1155/2020/9464389 |
| spellingShingle | Yuping Zeng Zhifeng Weng Fen Liang Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem Discrete Dynamics in Nature and Society |
| title | Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem |
| title_full | Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem |
| title_fullStr | Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem |
| title_full_unstemmed | Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem |
| title_short | Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem |
| title_sort | convergence analysis of h div conforming finite element methods for a nonlinear poroelasticity problem |
| url | http://dx.doi.org/10.1155/2020/9464389 |
| work_keys_str_mv | AT yupingzeng convergenceanalysisofhdivconformingfiniteelementmethodsforanonlinearporoelasticityproblem AT zhifengweng convergenceanalysisofhdivconformingfiniteelementmethodsforanonlinearporoelasticityproblem AT fenliang convergenceanalysisofhdivconformingfiniteelementmethodsforanonlinearporoelasticityproblem |