WEB-spline-based multigrid methods for the stationary stokes problem

We discuss a multigrid technique in solving a large system of linear algebraic equations arising in the approximation of Stokes equations by a new strategy based on weighted extended B-spline (WEB-spline) methods. Three types of WEB-spline-based Stokes elements satisfying the inf-sup condition are considered. First for a linear-constant type of Stokes element, we give the detailed multigrid algorithm and its convergence proof. The convergence proof of the multigrid algorithm for a bubble-stabilized WEB-spline-based Stokes element is dealt with separately. Multigrid method in the case of bubble-condensed variational form is simplified using the techniques from the bubble-stabilized case