THE COLLOCATION METHOD FOR MIXED BOUNDARY-VALUE-PROBLEMS ON DOMAINS WITH CURVED POLYGONAL BOUNDARIES

We consider an indirect boundary integral equation formulation for the mixed Dirichlet-Neumann boundary value problem for the Laplace equati on on a plane domain with a polygonal boundary. The resulting system o f integral equations is solved by a collocation method which uses a me sh grading transformation and a cosine approximating space. The mesh g rading transformation method yields fast convergence of the collocatio n solution by smoothing the singularities of the exact solution. A com plete stability and solvability analysis of the transformed integral e quations is given by use of a Mellin transform technique, in a setting in which each are of the polygon has associated with it a periodic So bolev space.