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2014 A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards’ Equation of van Genuchten-Mualem Model
Haitao Cao, Tao Yu, Xingye Yue
J. Appl. Math. 2014: 1-10 (2014). DOI: 10.1155/2014/657816

Abstract

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 C0 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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Haitao Cao. Tao Yu. Xingye Yue. "A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards’ Equation of van Genuchten-Mualem Model." J. Appl. Math. 2014 1 - 10, 2014. https://doi.org/10.1155/2014/657816

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010711
MathSciNet: MR3187048
Digital Object Identifier: 10.1155/2014/657816

Rights: Copyright © 2014 Hindawi

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