A two-grid block-centered finite difference method for nonlinear non-Fickian flow model

详细信息    查看全文

• 作者：Xiaoli Li ^{xiaolisdu@163.com" class="auth_mail" title="E-mail the corresponding author} ; Hongxing Rui ; ^{hxrui@sdu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Two-grid ; Block-centered finite difference ; Nonlinear ; Parabolic integro-differential equation ; Error estimates
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：30 April 2016
• 年：2016
• 卷：281
• 期：Complete
• 页码：300-313
• 全文大小：1016 K

文摘

In this paper, a two-grid block-centered finite difference scheme is introduced and analyzed to solve the nonlinear parabolic integro-differential equation arising in modeling non-Fickian flow in porous media. This method is considered where the nonlinear problem is solved only on a coarse grid of size H and a linear problem is solved on a fine grid of size h. Error estimates are established on non-uniform rectangular grid which show that the discrete L^∞(L²) and L²(H¹) errors are title="Click to view the MathML source">O(▵t+h²+H³)$O(▵t+h^2+H^3)$. Finally, some numerical experiments are presented to show the efficiency of the two-grid method and verify that the convergence rates are in agreement with the theoretical analysis.