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A connection between subgrid scale eddy viscosity and mixed methods. (English) Zbl 1024.76026
Summary: We consider a new mixed method (related to the EVSS method in computational viscoelasticity) for the convection-dominated, convection-diffusion equation in which stabilization is added then removed through the extra ‘mixed’ variables. This consistent stabilization is equivalent to an artificial viscosity operator acting only on the fluctuations in \(\nabla u^h\). By suitable choice of the mixed spaces, a method of Guermond [J.-L. Guermond, M2AN, Math. Model. Numer. Anal. 33, 1293-1316 (1999; Zbl 0946.65112)] is recovered exactly. We show that for a different, natural choice a new method results with global error estimates similar to both Guermond’s method and the streamline diffusion/SUPG method.

76M10 Finite element methods applied to problems in fluid mechanics
76R50 Diffusion
Full Text: DOI
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