An H(div)-Conforming Finite Element Method for the Biot Consolidation Model

An H(div)-Conforming Finite Element Method for the Biot Consolidation Model

Year:    2019

East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 3 : pp. 558–579

Abstract

An $H$(div)-conforming finite element method for the Biot's consolidation model is developed, with displacements and fluid velocity approximated by elements from BDM$k$ 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.170918.261218

East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 3 : pp. 558–579

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Poroelasticity mixed finite element H(div)-conforming discontinuous Galerkin method.