TY - JOUR
T1 - An H(div)-Conforming Finite Element Method for the Biot Consolidation Model
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 558
EP - 579
PY - 2019
DA - 2019/06
SN - 9
DO - http://doi.org/10.4208/eajam.170918.261218
UR - https://global-sci.org/intro/article_detail/eajam/13167.html
KW - Poroelasticity, mixed finite element, H(div)-conforming, discontinuous Galerkin method.
AB - <p style="text-align: justify;">An $H$(div)-conforming finite element method for the Biot&#39;s consolidation model is developed, with displacements and fluid velocity approximated by elements from
BDM<sub>$k$</sub> space. The use of $H$(div)-conforming elements for flow variables ensures the local
mass conservation. In the $H$(div)-conforming approximation of displacement, the tangential components are discretised in the interior penalty discontinuous Galerkin framework, and the normal components across the element interfaces are continuous. Having
introduced a spatial discretisation, we develop a semi-discrete scheme and a fully discrete scheme, prove their unique solvability and establish optimal error estimates for
each variable.</p>