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.
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