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Boundary element methods with wavelets and mesh refinement

by T. von Petersdorff and Ch. Schwab

(Report number 1995-10)

Abstract
We consider an elliptic boundary value problem in a polygonal domain. We propose a Galerkin boundary element method with wavelet basis functions. We show that the cost of the method is $O(N \log^k N)$ and yields the solution with the same convergence rates as the exact Galerkin method, including superconvergence in interior points. By adding finer wavelets only near certain vertices we can also compensate the effect of singularities in the solution.

Keywords: Integral equations, wavelets, mesh-refinement

@Techreport{vS95_80,
  author = {T. von Petersdorff and Ch. Schwab},
  title = {Boundary element methods with wavelets and mesh refinement},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1995-10},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1995/1995-10.pdf },
  year = {1995}
}

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