Volume 9, Issue 3
An H(div)-Conforming Finite Element Method for the Biot Consolidation Model

Yuping Zeng, Mingchao Cai & Feng Wang

East Asian J. Appl. Math., 9 (2019), pp. 558-579.

Published online: 2019-06

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M12, 65M15, 65M60, 74F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-558, author = {}, title = {An H(div)-Conforming Finite Element Method for the Biot Consolidation Model}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.170918.261218}, url = {http://global-sci.org/intro/article_detail/eajam/13167.html} }
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 -

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.

Yuping Zeng, Mingchao Cai & Feng Wang. (2019). An H(div)-Conforming Finite Element Method for the Biot Consolidation Model. East Asian Journal on Applied Mathematics. 9 (3). 558-579. doi:10.4208/eajam.170918.261218
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