Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (8): 1095-1112.doi: https://doi.org/10.1007/s10483-016-2120-8

• Articles • Previous Articles    

Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

Chao XU1, Dongyang SHI2, Xin LIAO2   

  1. 1. Faculty of Mathematics and Physics Education, Luoyang Institute of Science and Technology, Luoyang 471023, China;
    2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
  • Received:2015-10-09 Revised:2016-03-14 Online:2016-08-01 Published:2016-08-01
  • Contact: Dongyang SHI E-mail:shi_dy@zzu.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (No. 11271340)

Abstract:

This paper studies a low order mixed finite element method (FEM) for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q1rot element and the piecewise constant, respectively. The superconvergent error estimates of the velocity in the broken H1-norm and the pressure in the L2-norm are obtained respectively when the exact solutions are reasonably smooth. A numerical experiment is carried out to confirm the theoretical results.

Key words: constrained Q1rot nonconforming finite element (FE), nonstationary incompressible Navier-Stokes equation, superconvergent error estimate

2010 MSC Number: 

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