Global polynomial approximation for Symm's equation on polygons
The authors present a stability and convergence analysis of high order collocation methods for Symm's integral equation on curves with corners. The method is based on a mesh grading transformation of the original equation which ``spreads out'' the singularities at the corner points, followed by collocation with global algebraic polynomials for the transformed equation. This scheme offers an interesting alternative to known methods based on splines or trigonometric polynomials. Some numerical experiments are reported which illustrate the convergence results and show that the resulting linear systems are fairly well-conditioned.
scientific article; zbMATH DE number 1547999