Uniform Convergence of Galerkin Solutions to Non-compact Integral Operator Equations

Abstract

We consider a class of second-kind integral equations in which the operator is not compact. These may be solved numerically by a Galerkin method using piecewise polynomials as basis functions. Here we improve the existing stability analysis for such methods, and establish optimal rates of convergence for the Galerkin solution in the uniform norm. Also, superconvergence is established for the iterated Galerkin solution and for a suitably averaged Galerkin solution.