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Volume 36, Issue 4
A Weak Galerkin Finite Element Method for the Linear Elasticity Problem in Mixed Form

Ruishu Wang & Ran Zhang

DOI: 10.4208/jcm.1701-m2016-0733

J. Comp. Math., 36 (2018), pp. 469-491.

Published online: 2018-06

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  • Abstract

In this paper, we use the weak Galerkin (WG) finite element method to solve the mixed form linear elasticity problem. In the mixed form, we get the discrete of proximation of the stress tensor and the displacement field. For the WG methods, we define the weak function and the weak differential operator in an optimal polynomial approximation spaces. The optimal error estimates are given and numerical results are presented to demonstrate the efficiency and the accuracy of the weak Galerkin finite element method.

  • Keywords

Linear elasticity, mixed form, Korn's inequality, weak Galerkin finite element method.

  • AMS Subject Headings

65N30, 65N15, 65N12, 35J50, 74B05.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wangrs16@mails.jlu.edu.cn (Ruishu Wang)

zhangran@mail.jlu.edu.cn (Ran Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-469, author = {Wang , Ruishu and Zhang , Ran}, title = {A Weak Galerkin Finite Element Method for the Linear Elasticity Problem in Mixed Form}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {4}, pages = {469--491}, abstract = {

In this paper, we use the weak Galerkin (WG) finite element method to solve the mixed form linear elasticity problem. In the mixed form, we get the discrete of proximation of the stress tensor and the displacement field. For the WG methods, we define the weak function and the weak differential operator in an optimal polynomial approximation spaces. The optimal error estimates are given and numerical results are presented to demonstrate the efficiency and the accuracy of the weak Galerkin finite element method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1701-m2016-0733}, url = {http://global-sci.org/intro/article_detail/jcm/12301.html} }
TY - JOUR T1 - A Weak Galerkin Finite Element Method for the Linear Elasticity Problem in Mixed Form AU - Wang , Ruishu AU - Zhang , Ran JO - Journal of Computational Mathematics VL - 4 SP - 469 EP - 491 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1701-m2016-0733 UR - https://global-sci.org/intro/article_detail/jcm/12301.html KW - Linear elasticity, mixed form, Korn's inequality, weak Galerkin finite element method. AB -

In this paper, we use the weak Galerkin (WG) finite element method to solve the mixed form linear elasticity problem. In the mixed form, we get the discrete of proximation of the stress tensor and the displacement field. For the WG methods, we define the weak function and the weak differential operator in an optimal polynomial approximation spaces. The optimal error estimates are given and numerical results are presented to demonstrate the efficiency and the accuracy of the weak Galerkin finite element method.

Wang , Ruishu and Zhang , Ran. (2018). A Weak Galerkin Finite Element Method for the Linear Elasticity Problem in Mixed Form. Journal of Computational Mathematics. 36 (4). 469-491. doi:10.4208/jcm.1701-m2016-0733
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