Numerische Mathematik

, Volume 100, Issue 3, pp 485–518

Interior penalty method for the indefinite time-harmonic Maxwell equations

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

DOI: 10.1007/s00211-005-0604-7

Cite this article as:
Houston, P., Perugia, I., Schneebeli, A. et al. Numer. Math. (2005) 100: 485. doi:10.1007/s00211-005-0604-7

Summary

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 Open image in new window(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 Open image in new window(hℓ+1). The theoretical results are confirmed in a series of numerical experiments.

Mathematics Subject Classification (2000)

65N30 

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Paul Houston
    • 1
  • Ilaria Perugia
    • 2
  • Anna Schneebeli
    • 3
  • Dominik Schötzau
    • 4
  1. 1.Department of MathematicsUniversity of LeicesterLeicesterEngland
  2. 2.Dipartimento di MatematicaUniversità di PaviaPaviaItaly
  3. 3.Department of MathematicsUniversity of BaselBaselSwitzerland
  4. 4.Mathematics DepartmentUniversity of British ColumbiaVancouverCanada

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