Stabilized finite element methods with shock capturing for advection-diffusion problems

摘要

Stabilized FEM of streamline-diffusion type for advection-diffusion problems may exhibit local oscillations in crosswind direction (s). as a remedy, a sock-capturing variant of such stabilized schemes is considered as an additional consistent (but nonlinear) stabilization. We prove existence of discrete solutions. Then we present some a priori and a posteriori estimates. Finally we address the efficient solution of the arising nonlinear discrete problems.