Error Estimates of Mixed Finite Element Methods for Time-Fractional Navier–Stokes Equations

被引：2
作者：
Xiaocui Li
Xiaoyuan Yang
Yinghan Zhang
机构：
[1] Beihang University,Department of Mathematics, LMIB of the Ministry of Education
[2] University of Science and Technology Beijing,School of Mathematics and Physics
来源：
Journal of Scientific Computing | 2017年 / 70卷
关键词：
Time-fractional Navier–Stokes equations; Finite element method; Error estimates; Strong convergence; 60N15; 65M60; 60N30; 75D05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper studies the Galerkin finite element approximation of time-fractional Navier–Stokes equations. The discretization in space is done by the mixed finite element method. The time Caputo-fractional derivative is discretized by a finite difference method. The stability and convergence properties related to the time discretization are discussed and theoretically proven. Under some certain conditions that the solution and initial value satisfy, we give the error estimates for both semidiscrete and fully discrete schemes. Finally, a numerical example is presented to demonstrate the effectiveness of our numerical methods.
引用
收藏
页码：500 / 515
页数：15
相关论文
共 90 条
  • [1] Pani AK(2005)Semidiscrete finite element Galerkin approximations to the equations of motion arising in the Oldroyd model IMA J. Numer. Anal. 25 750-782
  • [2] Yuan JY(2015)Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion IMA J. Numer. Anal. 35 561-582
  • [3] Jin B(2012)Error estimates for a semidiscrete finite element method for fractional order parabolic equations SIAM J. Numer. Anal. 51 445-466
  • [4] Lazarov R(2015)The Galerkin finite element method for a multi-term time-fractional diffusion equation J. Comput. Phys. 281 825-843
  • [5] Pasciak J(2015)An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data IMA J. Numer. Anal. 33 691-698
  • [6] Zhou Z(2014)Spectral method for Navier–Stokes equations with slip boundary conditions J. Sci. Comput. 58 249-274
  • [7] Jin B(1985)A conforming finite element method for the time-dependent Navier–Stokes equations SIAM J. Numer. Anal. 22 455-473
  • [8] Lazarov R(2009)On the penalty-projection method for the Navier-Stokes equations with the MAC mesh J. Comput. Appl. Math. 226 228-245
  • [9] Zhou Z(2006)A second order accurate projection method for the incompressible Navier–Stokes equations on non-graded adaptive grids J. Comput. Phys. 219 912-929
  • [10] Jin B(2011)Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion Comput. Math. Appl. 62 855-875
123456789