A Mixed Formulation of Stabilized Nonconforming Finite Element Method for Linear Elasticity

A Mixed Formulation of Stabilized Nonconforming Finite Element Method for Linear Elasticity

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.

Author Details

Bei Zhang

Jikun Zhao