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A nonconforming scheme for non-Fickian flow in porous media
Peizhen Wang1, Liying Jiang2, Shaochun Chen3
1School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, 450011 China.
Abstract:
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.
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