  We develop a space-time mortar mixed finite element method for parabolic
problems. The domain is decomposed into a union of subdomains discretized with
non-matching spatial grids and asynchronous time steps. The method is based on
a space-time variational formulation that couples mixed finite elements in
space with discontinuous Galerkin in time. Continuity of flux (mass
conservation) across space-time interfaces is imposed via a coarse-scale
space-time mortar variable that approximates the primary variable. Uniqueness,
existence, and stability, as well as a priori error estimates for the spatial
and temporal errors are established. A space-time non-overlapping domain
decomposition method is developed that reduces the global problem to a
space-time coarse-scale mortar interface problem. Each interface iteration
involves solving in parallel space-time subdomain problems. The spectral
properties of the interface operator and the convergence of the interface
iteration are analyzed. Numerical experiments are provided that illustrate the
theoretical results and the flexibility of the method for modeling problems
with features that are localized in space and time.
