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

Guo, Benyu; Cao, Weiming

Bull. Greek Math. Soc. 32, 83-108 (1991).

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

Keywords:

periodicity; combined Fourier spectral-finite element schemes; error estimations; non-isotropic Sobolev space norms