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Spectral Tau approximation of the two-dimensional Stokes problem. (English) Zbl 0629.76037
We analyze the spectral-Tau method for the approximation of the Stokes system on a square. We precise which are the spurious modes for the discrete pressure and we prove an inf-sup condition. We provide an error estimate in the norm of the Sobolev spaces \(H^ s\), for the approximation of a divergence free vector field with polynomial divergence free vector fields. We apply these results to prove some convergence estimates for the solution of the discrete Stokes problem.

MSC:
76D07 Stokes and related (Oseen, etc.) flows
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
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