Volume 10, Issue 1
Stabilized Finite Element Methods for Biot's Consolidation Problems Using Equal Order Elements

Gang Chen & Minfu Feng

Adv. Appl. Math. Mech., 10 (2018), pp. 77-99.

Published online: 2018-10

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  • Abstract

Using the standard mixed Galerkin methods with equal order elements to solve Biot’s consolidation problems, the pressure close to the initial time produces large non-physical oscillations. In this paper, we propose a class of fully discrete stabilized methods using equal order elements to reduce the effects of non-physical oscillations. Optimal error estimates for the approximation of displacements and pressure at every time level are obtained, which are valid even close to the initial time. Numerical experiments illustrate and confirm our theoretical analysis.

  • Keywords

Biot’s problem, LBB condition, stabilized method, error estimates, numerical experiments, Terzaghi problem.

  • AMS Subject Headings

65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-77, author = {}, title = {Stabilized Finite Element Methods for Biot's Consolidation Problems Using Equal Order Elements}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {1}, pages = {77--99}, abstract = {

Using the standard mixed Galerkin methods with equal order elements to solve Biot’s consolidation problems, the pressure close to the initial time produces large non-physical oscillations. In this paper, we propose a class of fully discrete stabilized methods using equal order elements to reduce the effects of non-physical oscillations. Optimal error estimates for the approximation of displacements and pressure at every time level are obtained, which are valid even close to the initial time. Numerical experiments illustrate and confirm our theoretical analysis.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2016.m1182}, url = {http://global-sci.org/intro/article_detail/aamm/10502.html} }
TY - JOUR T1 - Stabilized Finite Element Methods for Biot's Consolidation Problems Using Equal Order Elements JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 77 EP - 99 PY - 2018 DA - 2018/10 SN - 10 DO - http://dor.org/10.4208/aamm.2016.m1182 UR - https://global-sci.org/intro/aamm/10502.html KW - Biot’s problem, LBB condition, stabilized method, error estimates, numerical experiments, Terzaghi problem. AB -

Using the standard mixed Galerkin methods with equal order elements to solve Biot’s consolidation problems, the pressure close to the initial time produces large non-physical oscillations. In this paper, we propose a class of fully discrete stabilized methods using equal order elements to reduce the effects of non-physical oscillations. Optimal error estimates for the approximation of displacements and pressure at every time level are obtained, which are valid even close to the initial time. Numerical experiments illustrate and confirm our theoretical analysis.

Gang Chen & Minfu Feng. (2020). Stabilized Finite Element Methods for Biot's Consolidation Problems Using Equal Order Elements. Advances in Applied Mathematics and Mechanics. 10 (1). 77-99. doi:10.4208/aamm.2016.m1182
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