A convergent multigrid cycle for the hybridized mixed method

We consider the application of a variable V-cycle multigrid algorithm for the hybridized mixed method for second order elliptic boundary value problems. Our algorithm differs from previous works on multigrid for the mixed method in that it is targeted at efficiently solving the matrix system for the Lagrange multiplier of the method. Since the mixed method is best implemented by first solving for the Lagrange multiplier and recovering the remaining unknowns locally, our algorithm is more useful in practice. The critical ingredient in the algorithm is a suitable intergrid transfer operator. We design such an operator and prove mesh independent convergence of the variable V-cycle algorithm. Numerical experiments indicating the asymptotically optimal performance of our algorithm, as well as the failure of certain seemingly plausible intergrid transfer operators, are presented. Copyright c © 2009 John Wiley & Sons, Ltd.