Generalized inf-sup conditions for Chebyshev spectral approximation of the Stokes problem. (English) Zbl 0666.76055

The Stokes flow problem and its approximations are considered in an abstract framework making use of a Galerkin method and a collocation method formulated in Chebyshev weighted Sobolev function spaces and their approximations. The Stokes problem has been transformed into a variational formulation in the continuous case and the finite-dimensional approximation and then a weighted variational formulation of the problem has been given in order to analyse a spectral Chebyshev approximation of the Stokes problem. The inf-sup conditions have been determined which are necessary and sufficient for the existence of a unique variational solution to the Stokes problem under consideration. A Galerkin spectral method is employed to discretize the problem and the spectral collocation method is analysed for the Stokes problem.
Reviewer: Z.Dżygadło


76D07 Stokes and related (Oseen, etc.) flows
35Q30 Navier-Stokes equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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