An adaptive boundary element method for the exterior
Stokes problem in three dimensions
Vincent J. Ervin and Norbert Heuer
IMA J. Numer. Anal., 26 (2), 297-325, 2006.
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 one-dimensional 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 an appendix we prove
optimal lower a priori error estimates for edge singularities on uniform
and graded meshes.