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This paper presents an arbitrary order locking-free numerical scheme forlinear elasticity on general polygonal/polyhedral partitions by using weakGalerkin (WG) finite element methods. Like other WG methods, the key idea forthe linear elasticity is to introduce discrete weak strain and stress tensorswhich are defined and computed by solving inexpensive local problems on eachelement. Such local problems are derived from weak formulations of thecorresponding differential operators through integration by parts. Locking-freeerror estimates of optimal order are derived in a discrete $H^1$-norm and theusual $L^2$-norm for the approximate displacement when the exact solution issmooth. Numerical results are presented to demonstrate the efficiency,accuracy, and the locking-free property of the weak Galerkin finite elementmethod.

A Locking-Free Weak Galerkin Finite Element Method for Elasticity Problems in the Primal Formulation