Classical solutions of two‐dimensional stokes problems on non‐smooth domains. Part 2: Collocation method for the radon equation

Abstract

AbstractThe 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.