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 entries, and by imposing a symmetry condition on this rule we ensure that the matrix is Hermitian (symmetric in the purely real case). As a specific application of our general theory we treat Symm's logarithmic-kernel equation, using piecewise-constant trial functions. Numerical experiments confirm that the quadrature errors do not degrade the rate of convergence of Galerkin's method. This result appears to hold even for non-smooth solutions if the mesh is suitably graded.