Stabilized finite element methods with shock capturing for advection-diffusion problems. (English) Zbl 1001.76058

Summary: Stabilized FEM of streamline-diffusion type for advection-diffusion problems may exhibit local oscillations in crosswind direction(s). As a remedy, we consider a shock-capturing variant of such stabilized schemes 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 arising nonlinear discrete problems.


76M10 Finite element methods applied to problems in fluid mechanics
76R99 Diffusion and convection
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