Remarks on Multilevel Bases for Divergence-Free Finite Elements

The connection between the multilevel factorization method recently proposed by Sarin and Sameh for solving mixed discretizations of the Stokes equation and hierarchical basis preconditioners is established. For the 2D triangular Taylor-Hood element, a local basis of divergence-free velocities and a preconditioning method are proposed that could be useful in fractional step methods.