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Tuning the mesh of a mixed method for the stream function. Vorticity formulation of the Navier-Stokes equations. (English) Zbl 0760.76041
Summary: We study a new mixed method for the Stokes and Navier-Stokes equations. The method uses two meshes, one very fine for \(\omega\) and a coarser one for \(\psi\). Error estimates show that boundary layers do not require to refine the mesh for the stream function \(\psi\) as much as for the vorticity \(\omega\) when the Reynolds number is large. We prove estimates and study implementation problems.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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