Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations
Hiptmair, R., Moiola, A. and Perugia, I. (2013) Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations. Mathematics of Computation, 82 (281). pp. 247-268. ISSN 1088-6842
To link to this article DOI: 10.1090/S0025-5718-2012-02627-5
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.