Semi-discrete Galerkin approximation of the single layer equation by general splines (Q1392761)

A semi-discrete Galerkin approximation method for an equation with a single layer operator is considered. For the trial and test spaces quite general piecewise polynomials on quasi-uniform meshes are used. It is shown that the semi-discrete Galerkin approximations are well posed. They converge at the same rate as the corresponding Galerkin approximation in the \(H^0\) and \(H^{-1}\) norms.