Multigrid methods for Mortar finite elements

Abstract

The framework of mortar methods [3,4] provides a powerful tool to analyze the coupling of different discretizations across subregion boundaries. We present an alternative Lagrange multiplier space without loosing the optimality of the a priori bounds [10]. By means of the biorthogonality between the nodal basis functions of our new Lagrange multiplier space and the finite element trace space, we derive a symmetric positive definite mortar formulation on the unconstrained product space. This new variational problem is the starting point for the application of our multigrid method. Level independent convergence rates for the W—cycle can be established, provided that the number of smoothing steps is large enough.