Spectral-Finite Element Method for Solving Three-Dimensional Unsteady Navier-Stokes Equations

This paper is devoted to the combined Fourier spectral and finite element approxima-tions of three-dimensional,semi-periodic,unsteady Navier-Stokes equations.Fourier spectralmethod and finite element method are employed in the periodic and non-periodic directionsrespectively.A class of fully discrete schemes are constructed with artificial compression.Stricterror estimations are proved.The analysis shows also that the classical two-dimensional velocity-pressure elements can be readily extended to solving such three-dimensional semi-periodic prob-lems,provided they satisfy the two-dimensional"inf-suf"condition.