Interior penalty method for the indefinite time-harmonic Maxwell equations

  • Authors:

  • Paul Houston;Ilaria Perugia;Anna Schneebeli;Dominik Schötzau

  • Affiliations:

  • Department of Mathematics, University of Leicester, LE1 7RH, Leicester, England;Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100, Pavia, Italy;Department of Mathematics, University of Basel, Rheinsprung 21, 4051, Basel, Switzerland;Mathematics Department, University of British Columbia, 121-1984 Mathematics Road, V6T 1Z2, Vancouver, Canada

  • Venue:
  • Numerische Mathematik
  • Year:
  • 2005

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Abstract

In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high-frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and the L2-norm. In particular, the error in the energy norm is shown to converge with the optimal order ** (hmin{s,ℓ}) with respect to the mesh size h, the polynomial degree ℓ, and the regularity exponent s of the analytical solution. Under additional regularity assumptions, the L2-error is shown to converge with the optimal order ** (hℓ+1). The theoretical results are confirmed in a series of numerical experiments.