期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 49, 期 1, 页码 264-284出版社
SIAM PUBLICATIONS
DOI: 10.1137/090761057
关键词
Helmholtz equation; wave propagation; discontinuous Galerkin methods; plane waves; p-version error analysis; duality estimates
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-w(2), w > 0. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Despres, 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.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据