Wang Peizhen, Jiang Liying, Chen Shaochun
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, 450011 China.
Department of Basic Science, Zhengzhou Vocational College of Finance and Taxation, Zhengzhou, 450048 China.
J Inequal Appl. 2017;2017(1):142. doi: 10.1186/s13660-017-1419-7. Epub 2017 Jun 19.
In this paper, we construct a semi-discrete scheme and a fully discrete scheme using the Wilson nonconforming element for the parabolic integro-differential equation arising in modeling the non-Fickian flow in porous media by the interior penalty method. Without using the conventional elliptic projection, which was an indispensable tool in the convergence analysis of finite element methods in previous literature, we get an optimal error estimate which is only determined by the interpolation error. Finally, we give some numerical experiments to show the efficiency of the method.
在本文中，我们针对通过内罚方法对多孔介质中非菲克流进行建模时出现的抛物型积分微分方程，使用威尔逊非协调元构造了一个半离散格式和一个全离散格式。在不使用传统椭圆投影（这是以往文献中有限元方法收敛性分析必不可少的工具）的情况下，我们得到了一个仅由插值误差决定的最优误差估计。最后，我们给出了一些数值实验来展示该方法的有效性。
