LEGENDRE SPECTRAL-FINITE ELEMENT METHOD FOR THE THREE-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION

摘要

This paper is devoted to the mixed Legendre spectral-finite element approximation of the three-dimensional, non-periodic, unsteady Navier-Stokes equations. A class of fully discrete schemes are constructed with artificial compression. The generalized stability and convergence are proved strictly on the assumption that the two-dimensional inf-sup condition of the finite element approximation is satisfied.