Exponential convergence of the h – p version BEM for mixed boundary value problems on polyhedrons
H. Holm, Matthias Maischak, Ernst Peter Stephan · Mathematical Methods in the Applied Sciences · 2008
Abstract We analyze the h – p version of the boundary element method for the mixed Dirichlet–Neumann problems of the Laplacian in polyhedral domains. Based on a regularity analysis of the solution in countably normed spaces, we show that the boundary element Galerkin solution of the h – p version converges exponentially fast on geometrically graded meshes (up to an additional term that converges algebraically with arbitrary high order). Copyright © 2008 John Wiley & Sons, Ltd.