A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation

作者：Wang, Chunmei; Wang, Junping^*; Wang, Ruishu; Zhang, Ran

来源：Journal of Computational and Applied Mathematics, 2016, 307: 346-366.

DOI：10.1016/j.cam.2015.12.015

• Weak Galerkin
• Finite element methods
• Weak divergence
• Weak gradient
• Linear elasticity
• Polyhedral meshes

This paper presents an arbitrary order locking-free numerical scheme for linear elasticity on general polygonal/polyhedral partitions by using weak Galerkin (WG) finite element methods. Like other WG methods, the key idea for the linear elasticity is to introduce discrete weak strain and stress tensors which are defined and computed by solving inexpensive local problems on each element. Such local problems are derived from weak formulations of the corresponding differential operators through integration by parts. Locking-free error estimates of optimal order are derived in a discrete H-1-norm and the usual L-2-norm for the approximate displacement when the exact solution is smooth. Numerical results are presented to demonstrate the efficiency, accuracy, and the locking free property of the weak Galerkin finite element method. Published by Elsevier B.V.

• 出版日期2016-12-1
• 单位南京师范大学; 国家自然科学基金委员会; 台州学院; 吉林大学