Exponential Time Integrators for Unsteady Advection–Diffusion Problems on Refined Meshes

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