Ernst P. Stephan

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This paper presents a posteriori error estimates for the hp{version of the boundary element method. We discuss two rst kind integral operator equations , namely Symm's integral equation and the integral equation with a hypersingular operator. The computable upper error bounds indicate an algorithm for the automatic hp{adaptive mesh{reenement. The eeciency(More)
This paper deals with the basic approximation properties of the h-p version of the boundary element method (BEM) in IR 3. We extend the results on the exponential convergence of the h-p version of the boundary element method on geometric meshes from problems in polygonal domains to problems in polyhedral domains. In 2D elliptic boundary value problems the(More)
We study a multilevel additive Schwarz method for the h-p version of the Galerkin boundary element method with geometrically graded meshes. Both hypersingular and weakly singular integral equations of the first kind are considered. As it is well known the h-p version with geometric meshes converges exponentially fast in the energy norm. However, the(More)
In this paper we discuss the BPX preconditioner for the single layer potential operator. We nd that the extrem eigenvalues of the preconditioner applied to the single layer potential operator are bounded independent of the number of unknowns. A description of an eecient implementation of the BPX algorithm is given.