This paper reviews the state of the art and discusses very recent mathematical developments in the field of adaptive boundary element methods. This includes an overview of available a posteriori error estimates as well as a state-of-the-art formulation of convergence and quasi-optimality of adaptive mesh-refining algorithms.
@article{arxiv.1402.0744,
title = {Adaptive Boundary Element Methods},
author = {Michael Feischl and Thomas Führer and Norbert Heuer and Michael Karkulik and Dirk Praetorius},
journal= {arXiv preprint arXiv:1402.0744},
year = {2014}
}