RESEARCH ARTICLE

Two-grid stabilized mixed finite element method for fully discrete reaction-diffusion equations

  • Sufang ZHANG 1 ,
  • Kaitai LI 2 ,
  • Hongen JIA , 1
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  • 1. College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
  • 2. College of Mathematics, Xi'an Jiaotong University, Xi'an 710049, China

Received date: 14 Feb 2015

Accepted date: 08 Sep 2016

Published date: 20 Feb 2017

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

Two-grid mixed finite element method is proposed based on backward Euler schemes for the unsteady reaction-diffusion equations. The scheme combines with the stabilized mixed finite element scheme by using the lowest equal-order pairs for the velocity and pressure. The space two-grid method is also used to reduce the time consuming. The benefits of this approach are to avoid the higher derivative, but to have more favorable stability, and to get the numerical solution of the two unknown variables simultaneously. Stability analysis and error estimates are given in this work. Finally, the theoretical results are verified by the numerical examples.

Cite this article

Sufang ZHANG , Kaitai LI , Hongen JIA . Two-grid stabilized mixed finite element method for fully discrete reaction-diffusion equations[J]. Frontiers of Mathematics in China, 2017 , 12(2) : 481 -492 . DOI: 10.1007/s11464-016-0604-1

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