A locking-free conforming discontinuous Galerkin finite element method for linear elasticity problems

Abstract

This paper proposes a locking-free conforming discontinuous Galerkin (CDG) numerical scheme for solving linear elasticity problems. By introducing the discrete weak strain and discrete weak stress tensors, this paper establishes two types of numerical methods based on the primal and mixed variational formulations. The weak differential operators are approximated using discontinuous polynomials on each local element. Locking-free error estimates of optimal order convergence are established in both the energy norm and the $L^2$-norm, demonstrating the locking-free property of the CDG schemes, which arises from their equivalence. Numerical results are presented to confirm the accuracy and locking-free property of the CDG schemes.