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

Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria

doi:10.1090/S0025-5718-2012-02627-5

Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations
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Math. Comp. 82 (2013), 247-268 Request permission

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.

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