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

作　　者：Sufang ZHANG Kaitai LI Hongen JIA 

机构地区：[1]College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China [2]College of Mathematics, Xi'an Jiaotong University, Xi'an 710049, China

出　　处：《Frontiers of Mathematics in China》2017年第2期481-492,共12页中国高等学校学术文摘·数学（英文）

基　　金：Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11401422, 11172194）, the Provincial Soft Science Foundation of Shaanxi Province （No. 2014041007）, and Provincial Science Foundation of Shanxi （Nos. 2014011005, 2015011001）.

摘　　要：Two-grid mixed finite element method is proposed based on backward guler 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 twogrid 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.Two-grid mixed finite element method is proposed based on backward guler 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 twogrid 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.

关 键 词：Reaction-diffusion equations stabilized mixed finite element two-grid full-discrete schemes 

分 类 号：O175.2[理学—数学] O241.82[理学—基础数学]