Year: 2009
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 2-3 : pp. 348–359
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-JCM-10370
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 2-3 : pp. 348–359
Published online: 2009-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: $hp$-version of the boundary element method Adaptive refinement Preconditioning Signorini contact.