Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates

Authors:
Marcus J. Grote;Anna Schneebeli;Dominik Schötzau
Affiliations:
Department of Mathematics, University of Basel, Rheinsprung 21, CH-4051 Basel, Switzerland;Department of Mathematics, University of Basel, Rheinsprung 21, CH-4051 Basel, Switzerland;Mathematics Department, University of British Columbia, 121-1984 Mathematics Road, Vancouver, BC, Canada, V6T 1Z2
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

We develop the symmetric interior penalty discontinuous Galerkin (DG) method for the time-dependent Maxwell equations in second-order form. We derive optimal a priori error estimates in the energy norm for smooth solutions. We also consider the case of low-regularity solutions that have singularities in space.