Two-level methods for the single layer potential in \(\mathbb{R}^3\)
The rough contents of this very elaborate paper are as follows: 0. Introduction, 1. Notations and preliminaries, 2. Spectral analysis for two level additive Schwarz operator, 3. A posteriori error estimate, 4. Adaptive refinement algorithm , 5. Numerical results and references. The authors consider weakly singular integral equations of the first kind on open surface pieces. They obtain approximate solutions using the \(h\)-version of the Galerkin boundary element method. Moreover they introduce two-level additive Schwarz operators for non-overlaping domain decompositions and estimate the condition numbers of these operators with respect to the meshsize. By use of the above operators they obtain an a posteriori error estimate. The theoretical results are illustrated by some numerical examples.
scientific article; zbMATH DE number 1160314
scientific article