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

A completely discrete heterogeneous multiscale finite element method for multiscale Richards equation of van Genuchten-Mualem model
Authors: Haitao Cao 0002; Tao Yu 0003; Xingye Yue;

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

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 byC0piecewise 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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Keywords

Error bounds for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, QA1-939, PDEs in connection with fluid mechanics, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
gold