Adaptive multilevel BEM for acoustic scattering

We study the h- and p-versions of the Galerkin boundary element method for integral equations of the first kind in 2D and 3D which result from the scattering of time harmonic acoustic waves at hard or soft scatterers. We derive an abstract a-posteriori error estimate for indefinite problems which is based on stable multilevel decompositions of our test and trial spaces. The Galerkin error is estimated by easily computable local error indicators and an adaptive algorithm for h- or p-adaptivity is formulated. The theoretical results are illustrated by numerical examples for hard and soft scatterers in 2D and 3D.