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Numerische Mathematik

, Volume 78, Issue 2, pp 211–258 | Cite as

Quadrature for \(hp\)-Galerkin BEM in \({\hbox{\sf l\kern-.13em R}}^3\)

  • Stefan A. Sauter
  • Christoph Schwab

Summary.

The Galerkin discretization of a Fredholm integral equation of the second kind on a closed, piecewise analytic surface \(\Gamma \subset \hbox{\sf l\kern-.13em R}^3\) is analyzed. High order, \(hp\)-boundary elements on grids which are geometrically graded toward the edges and vertices of the surface give exponential convergence, similar to what is known in the \(hp\)-Finite Element Method. A quadrature strategy is developed which gives rise to a fully discrete scheme preserving the exponential convergence of the \(hp\)-Boundary Element Method. The total work necessary for the consistent quadratures is shown to grow algebraically with the number of degrees of freedom. Numerical results on a curved polyhedron show exponential convergence with respect to the number of degrees of freedom as well as with respect to the CPU-time.

Mathematics Subject Classification (1991):65N38; 65N55 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Stefan A. Sauter
    • 1
  • Christoph Schwab
    • 2
  1. 1. Lehrstuhl Prakt. Mathematik, Mathematisches Seminar, Universität Kiel, D-24098 Kiel, Germany; e-mail: sas@numerik.uni-kiel.de DE
  2. 2. Seminar f. Appl. Mathematics, ETH-Zentrum, CH-8092 Zürich, Switzerland CH

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