Year: 2018
Author: Minghao Li, Dongyang Shi, Ying Dai
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2016.m1464
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 1 : pp. 100–113
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Elasticity MFEM residuals stabilization.