A Robust Discontinuous Galerkin High-Order Finite Element Method for Elasticity Problems with Interfaces

A robust discontinuous Galerkin (DC) finite element method is proposed for elasticity problems with interfaces, where the continuity across the interfaces is weakly enforced by using Nitsche's method. We employ a weighting for the interfacial consistency terms arising in the Nitsche variational form and present a detailed finite element formulation of this DC method. The stabilization parameter is evaluated by solving element level generalized eigenvalue problem for higher-order elements. Consequently, we give the choice of the weighting parameter that results in an estimate for the stabilization parameter such that the method remains well behaved in the pathological cases. The accuracy and robustness of the proposed method are then demonstrated through several numerical examples.