An Economical Finite Element Scheme for Navier-Stokes Equations

Abstract

In this paper, a new finite element scheme for Navier-Stokes equations is proposed, in which three different partitions (in the two dimensional case) are used to construct finite element subspaces of the velocity field and the pressure. The error estimate of the finite element than approximation is given. The precision of this new scheme has the same order as the scheme $Q_2/P_0$, but it is more economical that the scheme $Q_2/P_0$.