  This paper is focussed on the numerical resolution of diffusion advection and
reaction equations (DAREs) with special features (such as fractures, walls,
corners, obstacles or point loads) which globally, as well as locally, have
important effects on the solution. We introduce a multilevel and local time
solver of DAREs based on the discontinuous Galerkin (DG) method for the spatial
discreization and time stepping methods such as exponential time differencing
(ETD), exponential Rosenbrock (EXPR) and implicit Euler (Impl) methods. The
efficiency of our solvers is shown with several experiments on cyclic
voltammetry models and fluid flows through domains with fractures.
