Frontiers of Mathematics in China >
Two-grid stabilized mixed finite element method for fully discrete reaction-diffusion equations
Received date: 14 Feb 2015
Accepted date: 08 Sep 2016
Published date: 20 Feb 2017
Copyright
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.
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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