An adaptive boundary element method for the exterior Stokes problem in three dimensions

We present an adaptive refinement strategy for the h-version of the boundary element method with weakly singular operators on surfaces. The model problem deals with the exterior Stokes problem, and thus considers vector functions. Our error indicators are computed by local projections onto 1D subspaces defined by mesh refinement. These indicators measure the error separately for the vector components and allow for component-independent adaption. Assuming a saturation condition, the indicators give rise to an efficient and reliable error estimator. Also we describe how to deal with meshes containing quadrilaterals which are not shape regular. The theoretical results are underlined by numerical experiments. To justify the saturation assumption, in the Appendix we prove optimal lower a priori error estimates for edge singularities on uniform and graded meshes.