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Volume 10, Issue 1
New Residual Based Stabilization Method for the Elasticity Problem

Minghao Li, Dongyang Shi & Ying Dai

Adv. Appl. Math. Mech., 10 (2018), pp. 100-113.

Published online: 2018-10

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  • Abstract

In this paper, we consider the mixed finite element method (MFEM) of the elasticity problem in two and three dimensions (2D and 3D). We develop a new residual based stabilization method to overcome the inf-sup difficulty, and use Langrange elements to approximate the stress and displacement. The new method is unconditionally stable, and its stability can be obtained directly from Céa's lemma. Optimal error estimates for the $H^1$-norm of the displacement and $H$(div)-norm of the stress can be obtained at the same time. Numerical results show the excellent stability and accuracy of the new method.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-100, author = {Li , MinghaoShi , Dongyang and Dai , Ying}, title = {New Residual Based Stabilization Method for the Elasticity Problem}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {1}, pages = {100--113}, abstract = {

In this paper, we consider the mixed finite element method (MFEM) of the elasticity problem in two and three dimensions (2D and 3D). We develop a new residual based stabilization method to overcome the inf-sup difficulty, and use Langrange elements to approximate the stress and displacement. The new method is unconditionally stable, and its stability can be obtained directly from Céa's lemma. Optimal error estimates for the $H^1$-norm of the displacement and $H$(div)-norm of the stress can be obtained at the same time. Numerical results show the excellent stability and accuracy of the new method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2016.m1464}, url = {http://global-sci.org/intro/article_detail/aamm/10503.html} }
TY - JOUR T1 - New Residual Based Stabilization Method for the Elasticity Problem AU - Li , Minghao AU - Shi , Dongyang AU - Dai , Ying JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 100 EP - 113 PY - 2018 DA - 2018/10 SN - 10 DO - http://doi.org/10.4208/aamm.2016.m1464 UR - https://global-sci.org/intro/article_detail/aamm/10503.html KW - Elasticity, MFEM, residuals, stabilization. AB -

In this paper, we consider the mixed finite element method (MFEM) of the elasticity problem in two and three dimensions (2D and 3D). We develop a new residual based stabilization method to overcome the inf-sup difficulty, and use Langrange elements to approximate the stress and displacement. The new method is unconditionally stable, and its stability can be obtained directly from Céa's lemma. Optimal error estimates for the $H^1$-norm of the displacement and $H$(div)-norm of the stress can be obtained at the same time. Numerical results show the excellent stability and accuracy of the new method.

Minghao Li, Dongyang Shi & Ying Dai. (2020). New Residual Based Stabilization Method for the Elasticity Problem. Advances in Applied Mathematics and Mechanics. 10 (1). 100-113. doi:10.4208/aamm.2016.m1464
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