The hp-Version of the Boundary Element Method on Polygons

Norbert Heuer, Ernst P. Stephan
 J. Integral Equations Appl., 8 (2), 173-212, 1996.
Abstract
We give a new proof for the exponential convergence of the hp-version of the boundary element method for some first kind integral equations on polygons. Crucial for our analysis are asymptotic expansions of the solutions of the integral equations in terms of singularity functions near the vertices of the polygon. The boundary integral equations under consideration are Symm's integral equation with the logarithmic kernel and the hypersingular integral equation resulting from taking the normal derivative of the double layer potential. Applications to acoustic scattering problems and crack problems in linear elasticity are given.