A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

• Published in: Acta mathematica scientia Vol. 31; no. 2; pp. 367 - 382
• Main Author: 石东洋 任金城 龚伟
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2011; Department of Mathematics,Zhengzhou University,Zhengzhou 450052,China%Department of Mathematics,Shangqiu Normal University,Shangqiu 476000,China%Institute of Computational Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China
• Subjects: 65N15; 65N30; Approximation; Errors; Estimates; Finite element method; Mathematical analysis; Navier-Stokes equations; nonconforming mixed finite element; optimal order error estimates; Optimization; scheme; Stationary Navier-Stokes equations; Stokes方程; 常量元素; 数值试验; 有限元格式; 模误差估计; 混合有限元方法; 非协调; Stationary Navier-Stokes equations; 65N15; optimal order error estimates; scheme; nonconforming mixed finite element; 65N30; nonconforming mixed finite element scheme
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(11)60238-5

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.