Stabilization and adaptivity of transient convection-dominated convection diffusion problems
In this work we study a procedure to stabilize Galerkin finite element approximations to linear evolutionary convection-reaction-diffusion equations in the convection dominated regime. It is well known that standard finite element approximations to this kind of equations develop spurious oscillations when convection dominates diffusion. We propose a postprocessing that is able to eliminate spurious oscillations at a fixed time. The idea is the following. One first compute the standard Galerkin approximation at a given time and then solve a steady convection-reaction-diffusion problem with data based on the previously computed Galerkin approximation over the same finite element space but using the SUPG stabilized method. In the second part of the talk we propose an adaptive algorithm based on postprocessing that is able to compute an oscillation-free Galerkin approximation over an automatically adapted mesh that locates the smaller elements at the boundary layers.
This is a joint work with Javier de Frutos and Bosco García-Archilla