Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

Ralf Hiptmair, Andrea Moiola, I. Perugia

Publications: Contribution to journalArticlePeer Reviewed

Abstract

In this paper, we extend to the time-harmonic Maxwell equations the p-version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.
Original languageEnglish
Pages (from-to)247-268
Number of pages22
JournalMathematics of Computation
Volume82
Issue number281
DOIs
Publication statusPublished - 1 Jan 2013

Austrian Fields of Science 2012

  • 101014 Numerical mathematics

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