## 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.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76R50 Diffusion

Zbl 0946.65112
Full Text:

### References:

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