Report 1996-02

Quadrature for hp-Galerkin BEM in R^3

S.A. Sauter and C. Schwab

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

Paper: Available as PDF (27 MB) or as hardcopy to order reports@sam.math.ethz.ch.

Publishing information: In press in: Num. Math., (1997)