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.


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