Two-Level Method for the Single Layer Potential in R~3

摘要

We consider weakly singular integral equations of the first kind on open surface pieces Γ in R~3. To obtain approximate solutions we use the h-version Galerkin boundary element method. Further- more we introduce two-level additive Schwarz operators for non-overlapping domain decompositions of Γ and we estimate the conditions numbers of these operators with respect to the mesh size. Based on these operators we derive an a posteriori error estimate for the difference between the Exact solution and the Galerkinsolution. The estimate also involves the error which comes from an Approximate solution of the Galerkin equations.