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Knopp, T.; Lube, G.; Rapin, G.

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

Comput. Methods Appl. Mech. Eng. 191, No. 27-28, 2997-3013 (2002).
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.

Cited in 1 Review
Cited in 24 Documents

MSC:

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

Keywords:

advection-diffusion problems; existence of discrete solutions; shock-capturing stabilized schemes; a priori estimates; a posteriori estimates
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\textit{T. Knopp} et al., Comput. Methods Appl. Mech. Eng. 191, No. 27--28, 2997--3013 (2002; Zbl 1001.76058)
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