Weighted extended B-spline method for the approximation of the stationary Stokes problem

A new stabilized, mesh-free method for the approximation of the Stokes problem, using weighted extended B-splines (WEB-splines) as shape functions has been proposed. The web-spline based bilinear velocity–constant pressure element satisfies the so called inf–sup condition or Ladyshenskaya–Babus˘ka–Brezzi (LBB) condition. The main advantage of this method over standard finite element methods is that it uses regular grids instead of irregular partitions of domain, thus eliminating the difficult and time consuming pre-processing step. Convergence and Condition number estimates are derived. Numerical experiments in two space dimensions confirm the theoretical predictions.