  This paper is concerned with numerical solution of transport problems in
heterogeneous porous media. A semi-discrete continuous-in-time formulation of
the linear advection-diffusion equation is obtained by using a mixed hybrid
finite element method, in which the flux variable represents both the advective
and diffusive flux, and the Lagrange multiplier arising from the hybridization
is used for the discretization of the advective term. Based on global-in-time
and nonoverlapping domain decomposition, we propose two implicit local
time-stepping methods to solve the semi-discrete problem. The first method uses
the time-dependent Steklov-Poincar\'e type operator and the second uses the
optimized Schwarz waveform relaxation (OSWR) with Robin transmission
conditions. For each method, we formulate a space-time interface problem which
is solved iteratively. Each iteration involves solving the subdomain problems
independently and globally in time; thus, different time steps can be used in
the subdomains. The convergence of the fully discrete OSWR algorithm with
nonmatching time grids is proved. Numerical results for problems with various
Pecl\'et numbers and discontinuous coefficients, including a prototype for the
simulation of the underground storage of nuclear waste, are presented to
illustrate the performance of the proposed local time-stepping methods.
