LOCALIZATION AND POST PROCESSING
FOR THE GALERKIN BOUNDARY
ELEMENT METHOD APPLIED TO
THREE-DIMENSIONAL SCREEN PROBLEMS

ERNST P. STEPHAN AND THANH TRAN

Abstract:

We study local error estimates for various Galerkin schemes (Galerkin schemes with quasi-uniform or graded meshes, and the augmented Galerkin method) applied to weakly singular and hypersingular integral equations on open surfaces in ${\bf R}^3$. The results are given for a large scale of Sobolev norms, even in some norms that are not defined globally. In the case of the weakly singular integral equation where the highest orders of convergence achieved are in negative Sobolev norms, we establish from the Galerkin solutions new solutions that converge in the L²-norm to the exact solution in these orders.