Abstract: | This paper discusses a finite element approximation for an integral equation of the second kind deduced from a potential theory boundary value problem in two variables. The equation is shown to admit a unique solution, to be variational and coercive in the Hilbert space of functions σ ε H1/2(Γ), frd γ = 0. The Galerkin method with finite elements as trial functions is shown to lead to an optimal rate of convergence. |