Solution Algorithms for Mortar Mixed Finite Element Methods
       for Multiphase Flows in Porous Media


            Mary F. Wheeler and Ivan Yotov

      Texas Institute of Computational Mathematics
         The University of Texas at Austin,
                  Austin, Texas, USA

We consider mixed finite element approximations of systems of partial differential
equations describing multi-phase flow in porous media. 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 approximation of a reference pressure and molar densities.
The mortars serve as Lagrange multipliers for imposing flux-matching
conditions.

In this presentation we discuss solution algorithms for numerically
approximating the nonlinear algebraic system which arises from this
mixed finite element discretization.