Local error estimates and post processing for the Galerkin boundary element method on polygons

TL;DR

This paper develops local error estimates for the Galerkin boundary element method on polygons and introduces an averaging operator to enhance approximation accuracy.

Contribution

It provides new local Sobolev norm error estimates and a novel averaging technique to improve Galerkin boundary element solutions on polygonal domains.

Findings

Established local Sobolev error bounds for the Galerkin method.

Introduced the K-operator for averaging Galerkin solutions.

Demonstrated improved approximation quality using the K-operator.

Abstract

In this paper we give local error estimates in Sobolev norms for the Galerkin method applied to strongly elliptic pseudodifferential equations on a polygon. By using the K-operator, an operator which averages the values of the Galerkin solution, we construct improved approximations.