Year: 2020
Author: Bei Zhang, Jikun Zhao
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 278–300
Abstract
Based on the primal mixed variational formulation, a stabilized nonconforming mixed finite element method is proposed for the linear elasticity problem by adding the jump penalty term for the displacement. Here we use the piecewise constant space for stress and the Crouzeix-Raviart element space for displacement. The mixed method is locking-free, i.e., the convergence does not deteriorate in the nearly incompressible or incompressible case. The optimal convergence order is shown in the $L^2$-norm for stress and in the broken $H^1$-norm and $L^2$-norm for displacement, respectively. Finally, some numerical results are given to demonstrate the optimal convergence and stability of the mixed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0048
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 278–300
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Mixed method nonconforming finite element elasticity locking-free stabilization.
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