J. Comp. Math., Volume 26. A Mixed Finite Element Method on a Staggered Mesh for Navier-Stokes Equations Houde Han 1, Ming Yan 11 Department of Mathematics, University of Science and Technology of China, Hefei 230026, China Revised 2007-12-4 Accepted 2008-1-3 Online 2008-10-29 Abstract In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral $Q_1\times Q_1-P_0$ element approximation for the Navier-Stokes equations. First-order error estimates are obtained for both the velocity and the pressure. Numerical examples are presented to illustrate the effectiveness of the proposed method. Key words: Mixed finite element method, Staggered mesh, Navier-Stokes equations, Error estimate. AMS subject classifications: 35Q30, 74G15, 74S05. Email: hhan@math.tsinghua.edu.cn, yanm@math.ucla.edu