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Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation. (English) Zbl 0956.76040

Summary: The standard discretization of the Stokes and Navier-Stokes equations in vorticity and stream function formulation by affine finite elements is known for its bad convergence. We present here a modified discretization, prove that the convergence is improved, and establish a priori error estimates.

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
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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