A weighted Nitsche discontinuous Galerkin finite element method for plane problems

Abstract

The classical discontinuous Galerkin finite element method has the unstable numerical problem resulting from the inappropriate stability parameter for elasticity problem with interfaces. This problem can be released by the weighted Nitsche discontinuous Galerkin finite element method, but only for constant elements. To solve the above problems, the weights and the stabilization parameters of the weighted Nitsche discontinuous Galerkin finite element method are derived with four-node quadrilateral elements discretization for plane elasticity problems, and a qualitative dependence between the weights and the stabilization parameters is established. The weights and the stabilization parameters are evaluated automatically by setting up and solving generalized eigenvalue problems. This makes the use of high-order elements possible. The convergence and stability of the proposed method are verified through numerical examples. The results show that the weighted Nitsche discontinuous Galerkin finite element method has good stability and high accuracy for both homogeneous and heterogeneous problems in the material partition. In some extent, the method needs less manual work, and has high efficiency, high stability and better accuracy, making it suitable for solution of complicated interface problems.

Keywords

• elasticity
• discontinuous Galerkin finite element method
• weighted Nitsche method
• stability parameter
• interface problem
• high-order element