On local residual-type error estimates for boundary element methods

Abstract

Considering the Galerkin boundary element methods on smooth closed surfaces and the spline collocation method in the case of the curves, we estimate the local error of solution by a local residual together with a global term which can be expected to be small. This result shows that the local residual is a local error indicator. Except of the standard approximation properties, no special assumptions concerning mesh are needed. The results are given in the general framework of the pseudedifferential operators on closed smooth manifolds. Our work improves the recent results of Saranen and Wendland in many respects.

Keywords:

• Galerkin approximation
• pseudo-differential equations
• local estimates