.
MICHAEL GOLBERG
We show how to improve the estimate of the convergence rate of a number of
discrete polynomially-based Galerkin methods for Fredholm and Cauchy
singular integral equations. This has been accomplished by sharpening the
bounds on the quadrature errors in a manner analogous to that of Joe
[14] for spline-based methods. These results are then extended to
establish the convergence of some discrete Galerkin methods for
one-dimensional hypersingular equations and some boundary integral equations
on the sphere in .