Adaptive h-, p- and hp-versions for boundary integral element methods

Recently very promising results in a so-called hp-version of the finite element method have been obtained. The basic idea is a balanced combination of mesh refinement and increase of the polynomial degree of the shape functions. This idea is applied to a boundary collocation method in this paper. The new method is compared with adaptive h- and p-versions and it is shown in numerical examples that even in the presence of singularities in the exact solution exponential convergence is obtained.