Error analysis of the Bergman kernel method with singular basis   functions
  Let G be a bounded Jordan domain in the complex plane with piecewise analytic boundary. We present theoretical estimates and numerical evidence for certain phenomena, regarding the application of the Bergman kernel method with algebraic and pole singular basis functions, for approximating the conformal mapping of G onto the normalized disk. In this way, we complete the task of providing full theoretical justification of this method. 
M. Lytrides and N. Stylianopoulos
math.NA