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

Authors:
Stephanie Lohrengel;Serge Nicaise
Affiliations:
Laboratoire de Mathématiques, UFR Sciences Exactes et Naturelles, Université de Reims Champagne-Ardenne, Moulin de la Housse, 51687 Reims Cedex 2, France;Laboratoire MACS, Université de Valenciennes, Le Mont Houy, 59313 Valenciennes cedex 9, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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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.