| Abstract: | The non-uniquely solvable Radon boundary integral equation for the two-dimensional Stokes-Dirichlet problem on a non-smooth domain is transformed into a well posed one by a suitable compact perturbation of the velocity double-layer potential operator. The solution to the modified equation is decomposed into a regular part and a finite linear combination of intrinsic singular functions whose coefficients are computed from explicit formulae. Using these formulae, the classical collocation method, defined by continuous piecewise linear vector-valued basis functions, which converges slowly because of the lack of regularity of the solution, is improved into a collocation dual singular function method with optimal rates of convergence for the solution and for the coefficients of singularities. |
