A FULLY DISCRETE AND SYMMETRICAL BOUNDARY-ELEMENT METHOD

We study a fully discrete Galerkin method for a class of self-adjoint boundary integral equations on curves. The method uses a special type of composite two-dimensional integration rule to compute the matrix en tries, and by imposing a symmetry condition on this rule we ensure tha t the matrix is Hermitian (symmetric in the purely real case). As a sp ecific application of our general theory we treat Symm's logarithmic-k ernel equation, using piecewise-constant trial functions. Numerical ex periments confirm that the quadrature errors do not degrade the rate o f convergence of Galerkin's method. This result appears to hold even f or non-smooth solutions if the mesh is suitably graded.