  A space-time domain decomposition approach is presented as a natural
extension of the enhanced velocity mixed finite element (EVMFE) [Wheeler et.
al] for spatial domain decomposition. The proposed approach allows for
different space-time discretizations on non-overlapping, subdomains by
enforcing a mass continuity argument at the non-matching interface to preserve
the local mass conservation property inherent to the mixed finite element
methods. To this effect, we consider three different model formulations: (1) a
linear single phase flow problem, (2) a non-linear slightly compressible flow
and tracer transport, and (3) a non-linear slightly compressible, multiphase
flow and transport. We also present a numerical solution algorithm for the
proposed domain decomposition approach where a monolithic (fully coupled in
space and time) system is constructed that does not require subdomain
iterations. This space-time EVMFE method accurately resolves
advection-diffusion transport features, in a heterogeneous medium, while
circumventing non-linear solver convergence issues associated with large
time-step sizes for non-linear problems. Numerical results are presented for
the aforementioned, three, model formulations to demonstrate the applicability
of this approach to a general class of problems in flow and transport in porous
media.
