Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem

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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Main Authors: Yuping Zeng, Zhifeng Weng, Fen Liang
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2020/9464389
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spelling doaj-ccdd0f0cb1414dad96f0623e68af88662020-11-25T01:23:06ZengHindawi LimitedDiscrete 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
collection DOAJ
language English
format Article
sources DOAJ
author Yuping Zeng
Zhifeng Weng
Fen Liang
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
author_facet Yuping Zeng
Zhifeng Weng
Fen Liang
author_sort Yuping Zeng
title 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_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_sort convergence analysis of h(div)-conforming finite element methods for a nonlinear poroelasticity problem
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2020-01-01
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.
url http://dx.doi.org/10.1155/2020/9464389
work_keys_str_mv AT yupingzeng convergenceanalysisofhdivconformingfiniteelementmethodsforanonlinearporoelasticityproblem
AT zhifengweng convergenceanalysisofhdivconformingfiniteelementmethodsforanonlinearporoelasticityproblem
AT fenliang convergenceanalysisofhdivconformingfiniteelementmethodsforanonlinearporoelasticityproblem
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