  This work focuses on a class of elliptic boundary value problems with
diffusive, advective and reactive terms, motivated by the study of
three-dimensional heterogeneous physical systems composed of two or more media
separated by a selective interface. We propose a novel approach for the
numerical approximation of such heterogeneous systems combining, for the first
time: (1) a dual mixed hybrid (DMH) finite element method (FEM) based on the
lowest order Raviart-Thomas space (RT0); (2) a Three-Field (3F) formulation;
and (3) a Streamline Upwind/Petrov-Galerkin (SUPG) stabilization method. Using
the abstract theory for generalized saddle-point problems and their
approximation, we show that the weak formulation of the proposed method and its
numerical counterpart are both uniquely solvable and that the resulting finite
element scheme enjoys optimal convergence properties with respect to the
discretization parameter. In addition, an efficient implementation of the
proposed formulation is presented. The implementation is based on a systematic
use of static condensation which reduces the method to a nonconforming finite
element approach on a grid made by three-dimensional simplices. Extensive
computational tests demonstrate the theoretical conclusions and indicate that
the proposed DMH-RT0 FEM scheme is accurate and stable even in the presence of
marked interface jump discontinuities in the solution and its associated normal
flux. Results also show that in the case of strongly dominating advective
terms, the proposed method with the SUPG stabilization is capable of resolving
accurately steep boundary and/or interior layers without introducing spurious
unphysical oscillations or excessive smearing of the solution front.
