  In this paper, we study the stability and convergence of a decoupled and
linearized mixed finite element method (FEM) for incompressible miscible
displacement in a porous media whose permeability and porosity are
discontinuous across some interfaces. We show that the proposed scheme has
optimal-order convergence rate unconditionally, without restriction on the grid
ratio (between the time-step size and spatial mesh size). Previous works all
required certain restrictions on the grid ratio except for the problem with
globally smooth permeability and porosity. Our idea is to introduce an
intermediate system of elliptic interface problems, whose solution is uniformly
regular in each subdomain separated by the interfaces and its finite element
solution coincides with the fully discrete solution of the original problem. In
order to prove the boundedness of the fully discrete solution, we study the
finite element discretization of the intermediate system of elliptic interface
problems.
