@Article{JCM-27-348,
author = {Ernst P. Stephan},
title = {The $hp$-Version of BEM — Fast Convergence, Adaptivity and Efficient Preconditioning},
journal = {Journal of Computational Mathematics},
year = {2009},
volume = {27},
number = {2-3},
pages = {348--359},
abstract = {<p style="text-align: justify;">In this survey paper we report on recent developments of the $hp$-version of the boundary element method (BEM). As model problems we consider weakly singular and hypersingular integral equations of the first kind on a planar, open surface. We show that the Galerkin solutions (computed with the $hp$-version on geometric meshes) converge exponentially fast towards the exact solutions of the integral equations. An $hp$-adaptive algorithm is given and the implementation of the $hp$-version BEM is discussed together with the choice of efficient preconditioners for the ill-conditioned boundary element stiffness matrices. We also comment on the use of the $hp$-version BEM for solving Signorini contact problems in linear elasticity where the contact conditions are enforced only on the discrete set of Gauss-Lobatto points. Numerical results are presented which underline the theoretical results.</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/10370.html}
}