  Time integration of advection dominated advection-diffusion problems on
refined meshes can be a challenging task, since local refinement can lead to a
severe time step restriction, whereas standard implicit time stepping is
usually hardly suitable for treating advection terms. We show that exponential
time integrators can be an efficient, yet conceptually simple, option in this
case. Our comparison includes three exponential integrators and one
conventional scheme, the two-stage Rosenbrock method ROS2 which has been a
popular alternative to splitting methods for solving advection-diffusion
problems.
