TY - JOUR
T1 - Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations
AU - Hiptmair, Ralf
AU - Moiola, Andrea
AU - Perugia, I.
PY - 2013/1/1
Y1 - 2013/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84872192287&partnerID=8YFLogxK
U2 - 10.1090/S0025-5718-2012-02627-5
DO - 10.1090/S0025-5718-2012-02627-5
M3 - Article
AN - SCOPUS:84872192287
VL - 82
SP - 247
EP - 268
JO - Mathematics of Computation
JF - Mathematics of Computation
SN - 0025-5718
IS - 281
ER -