A Stabilized Hybrid Discontinuous Galerkin Method for Nearly Incompressible Linear Elasticity Problem

Abstract

In this work, a primal hybrid finite element method for nearly incom pressible linear elasticity problem on triangular meshes is shown. This method consists of coupling local discontinuous Galerkin problems to the primal variable with a global problem for the Lagrange multiplier, which is identified as the trace of the displacement field. Also, a local post-processing technique is used to recover stress approximations with improved rates of convergence in H(div) norm. Numerical studies show that the method is locking free even using equal or different orders for displacement and stress fields and optimal convergence rates are obtained.