Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods

Abstract

In this paper we introduce a discontinuous Galerkin method on polygonal meshes. This method arises from the discontinuous Galerkin composite finite element method (DGFEM) for source problems on domains with micro-structures. In the context of the present paper, the flexibility of DGFEM is applied to handle polygonal meshes. We prove the a priori convergence of the method for both eigenvalues and eigenfunctions for elliptic eigenvalue problems. Numerical experiments highlighting the performance of the proposed method for problems with discontinuous coefficients and on convex and non-convex polygonal meshes are presented.