BLOCK-CENTERED FINITE DIFFERENCE METHODS FOR NON-FICKIAN FLOW IN POROUS MEDIA

• 来源期刊: 计算数学（英文版）
• 关键词: Block-centered finite difference Parabolic integro-differential equation Non-uniform Error estimates Numerical analysis
• 年，卷（期）: 2018,（4）
• 页码范围: 492-516
• 页数: 25页
• 语种: 英文
• DOI: 10.4208/jcm.1701-m2016-0628

摘要

In this article,two block-centered finite difference schemes are introduced and analyzed to solve the parabolic integro-differential equation arising in modeling non-Fickian flow in porous media.One scheme is Euler backward scheme with first order accuracy in time increment while the other is Crank-Nicolson scheme with second order accuracy in time increment.Stability analysis and second-order error estimates in spatial meshsize for both pressure and velocity in discrete L2 norms are established on non-uniform rectangular grid.Numerical experiments using the schemes show that the convergence rates are in agreement with the theoretical analysis.