A Locking-Free Weak Galerkin Finite Element Method for Elasticity Problems in the Primal Formulation
Provides a locking-free numerical scheme for elasticity problems, addressing the volume locking issue in nearly incompressible materials for computational mechanics.
The paper develops an arbitrary order locking-free weak Galerkin finite element method for linear elasticity on general polygonal/polyhedral partitions, achieving optimal-order error estimates in discrete H1 and L2 norms for smooth solutions.
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.