A robust discontinuous Galerkin (DG) 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 DG 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.

中文翻译：

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具有界面的弹性问题的鲁棒间断 Galerkin 高阶有限元方法

针对具有界面的弹性问题，提出了一种稳健的不连续 Galerkin (DG) 有限元方法，其中通过使用 Nitsche 方法弱强制了跨界面的连续性。我们对 Nitsche 变分形式中出现的界面一致性项采用加权，并给出该 DG 方法的详细有限元公式。通过求解高阶单元的单元级广义特征值问题来评估稳定参数。因此，我们给出了对稳定参数进行估计的加权参数的选择，以使该方法在病理情况下仍然表现良好。然后通过几个数值例子证明了所提出方法的准确性和鲁棒性。