WEB-spline based mesh-free finite element analysis for the approximation of the stationary Navier–Stokes problem

The objective in this paper is to discuss the existence and the uniqueness of a weighted extended BB-spline (WEB-spline) based discrete solution for the stationary incompressible Navier–Stokes equations. The WEB-spline discretization is newly developed methodology which satisfies the inf–sup condition or Ladyshenskaya–Babus˘ka–Brezzi (LBB) condition. The main advantage of these new elements over standard finite elements is that they use regular grids instead of irregular partitions of the domain, thus eliminating the difficult and time-consuming pre-processing step. An error estimate for this WEB-spline based discrete solution is also obtained.