  The flux-mortar mixed finite element method was recently developed for a
general class of domain decomposition saddle point problems on non-matching
grids. In this work we develop the method for Darcy flow using the multipoint
flux approximation as the subdomain discretization. The subdomain problems
involve solving positive definite cell-centered pressure systems. The normal
flux on the subdomain interfaces is the mortar coupling variable, which plays
the role of a Lagrange multiplier to impose weakly continuity of pressure. We
present well-posedness and error analysis based on reformulating the method as
a mixed finite element method with a quadrature rule. We develop a
non-overlapping domain decomposition algorithm for the solution of the
resulting algebraic system that reduces it to an interface problem for the
flux-mortar, as well as an efficient interface preconditioner. A series of
numerical experiments is presented illustrating the performance of the method
on general grids, including applications to flow in complex porous media.
