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Spectral-finite element method for solving three-dimensional vorticity equations. (English) Zbl 0797.76041

Summary: We consider the numerical solution of the three-dimensional vorticity equations, which have the periodicity in one space direction. A class of combined Fourier spectral-finite element schemes is constructed. The computational work required by these schemes is relatively small, while higher accuracies can be expected. We prove error estimations in non- isotropic Sobolev space norms. A quite accurate estimation is obtained in the nonlinear case. The skills adopted are also applicable to other nonlinear problems.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D99 Incompressible viscous fluids
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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