About convergence of projection methods for solution of some Fredholm integral equations of the first kind

Abstract

This article is dedicated to research of approximation properties of B-splines and Lagrangian finite elements in Hilbert spaces of functions defined on surfaces in three-dimensional space. Hereinafter the conditions are determined for convergence of Galerkin and collocation methods for solving Fredholm integral equations of the first kind for simple layer potential that is equivalent to Dirichlet problem for Laplace equation in R3. Estimation is determined for the error of approximate solution of this problem obtained using potential theory methods.