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The full approximation accuracy for the stream function-vorticity- pressure method. (English) Zbl 0823.65110
The authors consider the stream function-vorticity-pressure formulation of the Stokes equations posed on a two-dimensional domain and its discretization by finite elements. They derive some error estimates; although these derivations do not explicitly require convexity of the domain, they do require high regularity of the (exact) solution of the Stokes equations (e.g., velocity in \(H^ k\) and pressure in \(H^{k - 2}\) for \(k \geq 4\)).
Reviewer: A.J.Meir (Auburn)

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
65N15 Error bounds for boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows
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