Fully discrete Galerkin methods for systems of boundary integral equations
The author considers a class of systems of boundary integral equations of the first kind, coupled with some side conditions of integral type and including some additional scalar unknowns, in order to guarantee the existence and uniqueness of the solution. The stability and convergence of a spline Galerkin method is then considered. He also proves the existence of a kind of asymptotic expansion of the error in the powers of the discretized parameter. The core of the paper is a generalization of the classical Galerkin collocation method in the sense that the method uses splines of arbitrary degree and a wider choice of quadrature formulae. An asymptotic expansion of the consistency error for this method is also carried out. The author ends the paper with a postprocessing which includes the computation of the solution of the boundary value problem associated to the boundary integral equation.
scientific article; zbMATH DE number 1043290
scientific article