Multigrid on the interface for mortar mixed finite element methods for elliptic problems

We consider mixed finite element approximations of second order elliptic eq uations on domains that can be described as a union of subdomains or blocks . We assume that the subdomain grids are locally defined and need not match across the block boundaries. Specially chosen mortar finite element spaces are introduced on the interfaces for approximating the scalar variable (pr essure). The mortars also serve as Lagrange multipliers for imposing flux-m atching conditions. The method is implemented by reducing the algebraic sys tem to a positive definite interface problem in the mortal spaces. This pro blem is then solved using a multigrid on the interface with conjugate gradi ent smoothing. The algorithm is very efficient in a distributed parallel co mputing environment as only subdomain solves are required on each conjugate gradient iteration. The standard variational assumptions for the multigrid are not satisfied, since the interface bilinear forms vary from level to l evel. We present theoretical results for the convergence of the V-cycle and the W-cycle. Computational results in two- and three-dimensions are given to illustrate and confirm the theory. (C) 2000 Elsevier Science S.A. All ri ghts reserved.