A discontinuous Galerkin method on refined meshes for the two-dimensional time-harmonic Maxwell equations in composite materials

Abstract

In this paper, a discontinuous Galerkin method for the two-dimensional time-harmonic Maxwell equations in composite materials is presented. The divergence constraint is taken into account by a regularized variational formulation and the tangential and normal jumps of the discrete solution at the element interfaces are penalized. Due to an appropriate mesh refinement near exterior and interior corners, the singular behaviour of the electromagnetic field is taken into account. Optimal error estimates in a discrete energy norm and in the L 2 -norm are proved in the case where the exact solution is singular.