An adaptive finite element method for evolutionary convection dominated problems

We present an adaptive finite element method for evolutionary convection–diffusion problems. The algorithm is based on an a posteriori indicator of the size of the oscillations displayed by the finite element approximation. The procedure is able to refine or coarsen dynamically the mesh adjusting it automatically to evolving layers. The method produces nearly non-oscillatory approximations in the convection dominated regime. We check the performance of the adaptive method with some numerical experiments.

► An adaptive FEM for evolutionary convection dominated problems is presented.
► A postprocessed approximation is used to define an indicator of the oscillation size.
► The a posteriori indicator is used to dynamically refine or coarsen the mesh.
► The method produces nearly non-oscillatory approximations.
► Numerical experiments are used to check the good behaviour of the method.