research-article

Modeling and Analysis of the Coupling in Discrete Fracture Matrix Models

Authors:

Martin J. Gander,

Julian Hennicker,

Roland MassonAuthors Info & Claims

SIAM Journal on Numerical Analysis, Volume 59, Issue 1

Pages 195 - 218

https://doi.org/10.1137/20M1312125

Published: 01 January 2021 Publication History

Abstract

This paper deals with the derivation and analysis of reduced order elliptic PDE models on fractured domains. We use a Fourier analysis to obtain coupling conditions between subdomains when the fracture is represented as a hypersurface embedded in the surrounded rock matrix. We compare our results to prominent examples from the literature for diffusive models. In a second step, we present error estimates for the reduced order models in terms of the fracture width. For the proofs, we rely on a combination of Fourier analysis, asymptotic expansions, and functional analysis. Finally, we study the behavior of the error of the reduced order solutions on numerical test cases when the fracture width tends to zero.

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Cited By

Huynh PCao YHoang T(2023)Fast and Accuracy-Preserving Domain Decomposition Methods for Reduced Fracture Models with Nonconforming Time GridsJournal of Scientific Computing10.1007/s10915-023-02251-096:1Online publication date: 29-May-2023
https://dl.acm.org/doi/10.1007/s10915-023-02251-0

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Published In

cover image SIAM Journal on Numerical Analysis

SIAM Journal on Numerical Analysis Volume 59, Issue 1

2021

584 pages

ISSN:0036-1429

DOI:10.1137/sjnaam.59.1

Issue’s Table of Contents

© 2021, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2021

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Cited By

Huynh PCao YHoang T(2023)Fast and Accuracy-Preserving Domain Decomposition Methods for Reduced Fracture Models with Nonconforming Time GridsJournal of Scientific Computing10.1007/s10915-023-02251-096:1Online publication date: 29-May-2023
https://dl.acm.org/doi/10.1007/s10915-023-02251-0

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