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.


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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