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 language | English |
---|---|
Pages (from-to) | 247-268 |
Number of pages | 22 |
Journal | Mathematics of Computation |
Volume | 82 |
Issue number | 281 |
DOIs | |
Publication status | Published - 1 Jan 2013 |
Austrian Fields of Science 2012
- 101014 Numerical mathematics