Stabilized FEM with shock-capturing for advection-diffusion problems

Stabilized FEM of streamline-diffusion type to advection-diffusion problems may exhibit local oscillations in crosswind direction(s). As a remedy, a shock-capturing variant is considered as an additional consistent (but nonlinear) stabilization. We present some preliminary results of the numerical analysis. The shock-capturing method has been applied within the numerical solution of the k/epsilon turbulence model of incompressible flow problems for the arising nonlinear advection-diffusion problems.