# Realization of hp-Galerkin BEM in R³

Sauter, S; Schwab, C (1996). Realization of hp-Galerkin BEM in R³. In: Hackbusch, W; Wittum, G. Boundary elements: implementation and analysis of advanced algorithms (Kiel, 1996). Braunschweig: Vieweg, 194-206.

## Abstract

t is well known that Galerkin discretizations based on hp-finite element spaces are converging exponentially with respect to the degrees of freedom for elliptic problems with piecewise analytic data. However, the question whether these methods can be realized for general situations such that the exponential convergence is preserved also with respect to the computing time is very essential.
We show how the numerical quadrature can be realized in order that the resulting fully discrete hp-boundary element method (BEM) converges exponentially with algebraically growing work. The key point is to approximate the integrals constituting the stiffness matrix by exponentially converging cubature methods.

## Abstract

t is well known that Galerkin discretizations based on hp-finite element spaces are converging exponentially with respect to the degrees of freedom for elliptic problems with piecewise analytic data. However, the question whether these methods can be realized for general situations such that the exponential convergence is preserved also with respect to the computing time is very essential.
We show how the numerical quadrature can be realized in order that the resulting fully discrete hp-boundary element method (BEM) converges exponentially with algebraically growing work. The key point is to approximate the integrals constituting the stiffness matrix by exponentially converging cubature methods.