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The Scientific World Journal
Volume 2013 (2013), Article ID 756281, 11 pages
Research Article

A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

1School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China
2School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Received 26 April 2013; Accepted 3 June 2013

Academic Editors: W.-S. Du and T. Ozawa

Copyright © 2013 Jinfeng Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient belongs to the weaker space taking the place of the classical space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in and -norm for both the scalar unknown and the diffusion term and a priori error estimates in -norm for its gradient for both semi-discrete and fully discrete schemes.