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In this paper we consider a quadrature method for a hypersingular integral equation arising from a boundary integral formulation for the Neumann problem in a two-dimensional domain with smooth boundary. We prove that this method is equivalent to the trigonometric.Galerkin method. Consequently, we obtain stability and asymptotic error estimates in the scale of Sobolev spaces. Finally, we present some numerical tests.

On a Full Discretization Scheme for a Hypersingular Boundary Integral Equation over Smooth Curves