Author(s)

M.A. Golberg

Abstract

We show how to obtain almost optimal convergence rates for discrete Galerkin methods for a number of Fredholm and singular integral equations. These rates improve on previous ones we have obtained for one-dimensional Fred- holm equations and are new for singular and multidimensional Fredholm equations. 1 Introduction The reformulation of boundary value problems leads to a variety of in- tegral equations. These include one-dimensional Fredholm equations [1], Cauchy singular equations [2], hypersingular equations [3] and multidimen- sional Fredholm equations [4]. Traditionally in the BEM literature these equations are solved numerically by piecewise polynomial collocation meth- ods [5]. However, there are many situations where global approximations based on polynomials for one-dimensional equations and spherical harmon- ics for surface integral equations are natural [

Keywords