Journal of Applied Mathematics

A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards’ Equation of van Genuchten-Mualem Model

Haitao Cao, Tao Yu, and Xingye Yue

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We propose a fully discrete method for the multiscale Richards’ equation of van Genuchten-Mualem model which describes the flow transport in unsaturated heterogenous porous media. Under the framework of heterogeneous multiscale method (HMM), a fully discrete scheme combined with a regularized procedure is proposed. Including the numerical integration, the discretization is given by C 0 piecewise finite element in space and an implicit scheme in time. Error estimates between the numerical solution and the solution of homogenized problem are derived under the assumption that the permeability is periodic. Numerical experiments with periodic and random permeability are carried out for the van Genuchten-Mualem model of Richards’ equation to show the efficiency and accuracy of the proposed method.

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J. Appl. Math., Volume 2014 (2014), Article ID 657816, 10 pages.

First available in Project Euclid: 2 March 2015

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Cao, Haitao; Yu, Tao; Yue, Xingye. A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards’ Equation of van Genuchten-Mualem Model. J. Appl. Math. 2014 (2014), Article ID 657816, 10 pages. doi:10.1155/2014/657816.

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