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

Preview Full PDF 508 1433
Export citation
  • 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 C´ea’s lemma. Optimal error estimates for the H1 -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.

  • Keywords

Elasticity, MFEM, residuals, stabilization.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-10-100, author = {}, 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 C´ea’s lemma. Optimal error estimates for the H1 -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 JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 100 EP - 113 PY - 2018 DA - 2018/10 SN - 10 DO - http://dor.org/10.4208/aamm.2016.m1464 UR - https://global-sci.org/intro/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 C´ea’s lemma. Optimal error estimates for the H1 -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
Copy to clipboard
The citation has been copied to your clipboard