ERROR ANALYSIS OF TREFFTZ-DISCONTINUOUS GALERKIN METHODS FOR THE TIME-HARMONIC MAXWELL EQUATIONS

作者：Hiptmair Ralf^*; Moiola Andrea; Perugia Ilaria

来源：Mathematics of Computation, 2013, 82(281): 247-268.

• Time-harmonic Maxwell%26apos
• s equation
• discontinuous Galerkin methods
• Trefftz methods
• p-version error analysis
• duality estimates
• plane waves

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.

• 出版日期2013-1