 
Summary: Solving a Single Layer Integral Equation
On Surfaces in R3
Yan Chen and Kendall Atkinson
Department of Mathematics
University of Iowa
Iowa City, IA 52242
January 27, 1994
Abstract
In this paper, we consider solving the single layer integral equa
tion (3) on a closed surface in R3. The numerical method is based on
Galerkin's method with spherical polynomials as the approximation
ing functions. We study the error of the approximating solution in
suitable Sobolev spaces.
Key Words: Spherical polynomials, Sobolev space, Galerkin's method.
AMS (MOS) Subject Classi cation: 65R20.
1 Introduction
Consider the solution of the following Dirichlet problem:
(
4u = 0 in
u = u0 on ; (1)
