  In this paper a new primal-dual mixed finite element method is introduced,
aimed to model multiscale problems with several geometric subregions in the
domain of interest. In each of these regions porous media fluid flow takes
place, but governed by physical parameters at a different scale; additionally,
a fluid exchange through contact interfaces occurs between neighboring regions.
The well-posedness of the primal-dual mixed finite element formulation on
bounded simply connected polygonal domains of the plane is presented. Next, the
convergence of the discrete solution to the exact solution of the problem is
discussed, together with the convergence rate analysis. Finally, the numerical
examples illustrate the method's capabilities to handle multiscale problems and
interface discontinuities as well as experimental rates of convergence.
