Ep. Stephan, THE H-P BOUNDARY-ELEMENT METHOD FOR SOLVING 2-DIMENSIONAL AND 3-DIMENSIONAL PROBLEMS, Computer methods in applied mechanics and engineering, 133(3-4), 1996, pp. 183-208
In this survey paper we report on recent developments of the hp-versio
n of the boundary element method. We consider weakly singular and hype
rsingular integral equations on polygons and polyhedral surfaces. We s
how that the Galerkin solutions (computed with the hp-version on geome
tric meshes) converge exponentially fast towards the exact solutions o
f the integral equations. The implementation of the hp-version of the
boundary element method is discussed and adaptive algorithms are given
. Model problems for the coupling of finite elements and boundary elem
ents are also considered. Numerical results are presented which underl
ine tile theoretical results.