Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the $p$-version

Hiptmair, R., Moiola, A. and Perugia, I. (2011) Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the $p$-version. SIAM Journal on Numerical Analysis (SINUM), 49 (1). pp. 264-284. ISSN 0036-1429 doi: 10.1137/090761057

Abstract/Summary

Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator $-\Delta-\omega^2$, $\omega>0$. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Després, SIAM J. Numer. Anal., 35 (1998), pp. 255–299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of $p$-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121–136], and plane wave approximation theory.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/28020
Identification Number/DOI	10.1137/090761057
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Society for Industrial and Applied Mathematics
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