Open AccessAn H(div)-Conforming Finite Element Method for the Biot Consolidation Model
Author(s) -
Yuping Zeng,
Mingchao Cai,
Feng Wang
Publication year - 2019
Publication title -
east asia journal on applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.421
H-Index - 17
eISSN - 2079-7370
pISSN - 2079-7362
DOI - 10.4208/eajam.170918.261218
Subject(s) - biot number , discretization , uniqueness , finite element method , poromechanics , mathematics , discontinuous galerkin method , mixed finite element method , consolidation (business) , mathematical analysis , displacement (psychology) , porous medium , physics , mechanics , materials science , structural engineering , engineering , accounting , porosity , business , composite material , psychology , psychotherapist
In this paper, we develop an H(div)-conforming finite element method for Biot's consolidation model in poroelasticity. In our method, the flow variables are discretized by an H(div)-conforming mixed finite elements. For relaxing the H 1 -conformity of the displacement, we approximate the displacement by using an H(div)-conforming finite element method, in which the tangential components are discretized in the interior penalty discontinuous Galerkin framework. For both the semi-discrete and the fully discrete schemes, we prove the existence and uniqueness theorems of the approximate solutions and derive the optimal convergence rate for each variable.