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We consider weakly singular integral equations of the rst kind on screens in IR 3. To obtain approximate solutions we use the hand p-versions of the Galerkin Boundary Element Method. We introduce two-level additive Schwarz operators with bounded condition numbers. Based on these operators we derive an a posteriori error estimate for the diierence between(More)
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)
We study the boundary element method for weakly singular and hypersingular integral equations of the first kind on screens resulting from the Dirichlet and Neumann problems for the Helmholtz equation. It is shown that the hp-version with geometrical refined meshes converges exponentially fast in both cases. We underline our theoretical results by numerical(More)
We consider weakly singular integral equations of the first kind on open surface pieces Γ in ℝ3. To obtain approximate solutions we use theh-version Galerkin boundary element method. Furthermore we introduce two-level additive Schwarz operators for non-overlapping domain decompositions of Γ and we estimate the conditions numbers of these operators with(More)