Multigrid for the mortar finite element method

A multigrid technique for uniformly preconditioning linear systems arising from a mortar finite element discretization of second order elliptic bounda ry value problems is described and analyzed. These problems are posed on do mains partitioned into subdomains, each of which is independently triangula ted in a multilevel fashion. The multilevel mortar finite element spaces ba sed on such triangulations (which need not align across subdomain interface s) are in general not nested. Suitable grid transfer operators and smoother s are developed which lead to a variable V-cycle preconditioner resulting i n a uniformly preconditioned algebraic system. Computational results illust rating the theory are also presented.