Numerische Mathematik

, Volume 66, Issue 1, pp 67–95 | Cite as

On quadrature methods for the double layer potential equation over the boundary of a polyhedron

  • A. Rathsfeld


In this paper we consider a quadrature method for the solution of the double layer potential equation corresponding to Laplace's equation in a threedimensional polyhedron. We prove the stability for our method in case of special triangulations over the boundary of the polyhedron. The assumptions imposed on the triangulations are analogous to those appearing in the one-dimensional case. Finally, we establish the rates of convergence and discuss the effect of mesh refinement near the corners and edges of the polyhedron.

Mathematics Subject Classification (1991)

45L10 65R20 


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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • A. Rathsfeld
    • 1
  1. 1.Institut für Angewandte Analysis und StochastikBerlinGermany

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