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Quadrature for hp-Galerkin BEM in R3

by S. A. Sauter and Ch. Schwab

(Report number 1996-02)

Abstract
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, emhp-/emboundary 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 emhp/em -Finite Element Method. A quadrature strategy is developed which gives rise to a fully discrete scheme preserving the exponential convergence of the emhp/em-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.

Keywords: emhp/em Finite Element, Boundary Element Method, Numerical Integration, exponential convergence

@Techreport{SS96_185,
  author = {S. A. Sauter and Ch. Schwab},
  title = {Quadrature for hp-Galerkin BEM in R3},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-02.pdf },
  year = {1996}
}

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