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

Sufang ZHANG, Kaitai LI, Hongen JIA

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PDF(370 KB)
Front. Math. China ›› 2017, Vol. 12 ›› Issue (2) : 481-492. DOI: 10.1007/s11464-016-0604-1
RESEARCH ARTICLE
RESEARCH ARTICLE

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

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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.

Keywords

Reaction-diffusion equations / stabilized mixed finite element / two-grid / full-discrete schemes

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Sufang ZHANG, Kaitai LI, Hongen JIA. Two-grid stabilized mixed finite element method for fully discrete reaction-diffusion equations. Front. Math. China, 2017, 12(2): 481‒492 https://doi.org/10.1007/s11464-016-0604-1

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