Open AccessConvergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem
Author(s) -
Yuping Zeng,
Zhifeng Weng,
Fen Liang
Publication year - 2020
Publication title -
discrete dynamics in nature and society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.264
H-Index - 39
eISSN - 1607-887X
pISSN - 1026-0226
DOI - 10.1155/2020/9464389
Subject(s) - finite element method , poromechanics , discretization , discontinuous galerkin method , nonlinear system , mixed finite element method , mathematics , convergence (economics) , a priori and a posteriori , displacement (psychology) , extended finite element method , galerkin method , mathematical analysis , mathematical optimization , porous medium , physics , geology , quantum mechanics , porosity , economic growth , economics , psychotherapist , thermodynamics , psychology , philosophy , geotechnical engineering , epistemology
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.