An overdetermined B-spline collocation method for Poisson problems on complex domains

The aim of this work is to show how the B-spline collocation method may be used for the approximate solution of Poisson problems considered on complex shaped planar domains in a simple and stable way. The most important aspect of this work consists in the use of approximate Fekete points recently developed by Sommariva and Vianello. Numerical experiments concerning the collocation solution of Poisson problems defined on an amoeba-like domain, star shaped domain and a square with eight holes subject to Dirichlet boundary conditions are presented.