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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received April 22, 1996
Rights and permissions
About this article
Cite this article
Sauter, S., Schwab, C. Quadrature for \(hp\)-Galerkin BEM in \({\hbox{\sf l\kern-.13em R}}^3\) . Numer. Math. 78, 211–258 (1997). https://doi.org/10.1007/s002110050311
Issue Date:
DOI: https://doi.org/10.1007/s002110050311