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

Chunmei Wang, Junping Wang, Ruishu Wang, Ran Zhang

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

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 H1-norm and the usual L2-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.

Original languageEnglish
Pages (from-to)346-366
Number of pages21
JournalJournal of Computational and Applied Mathematics
Volume307
DOIs
StatePublished - Dec 1 2016

Keywords

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

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