Finite element approximations in projection methods for solution of some Fredholm integral equation of the first kind
Approximation properties of B-splines and Lagrangian finite elements in Hilbert spaces of functions defined on surfaces in three-dimensional space are investigated. The conditions for the convergence of Galerkin and collocation methods for solution of the Fredholm integral equation of the first kind for the simple layer potential that is equivalent to the Dirichlet problem for Laplace equation in $\mathbb{R}^3$ are established. The estimation of the error of approximate solution of this problem, obtained by means of the potential theory methods, is determined.