Higher-Order Multiscale Computational Method for Multi-Continuum Problems in Highly Heterogeneous Media

Fuente: arXiv
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Hauptverfasser: Dong, Hao, Peng, Jiayuan, Huang, Jian
Format: Preprint
Veröffentlicht: 2026
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author Dong, Hao
Peng, Jiayuan
Huang, Jian
author_facet Dong, Hao
Peng, Jiayuan
Huang, Jian
contents This paper presents a high-accuracy higher-order multiscale method for solving multi-continuum problems in in highly heterogeneous media. First, microscopic unit cell functions are defined, leading to the derivation of macroscopic homogenized equations and formulas for calculating effective parameters, which yield a higher-order multi-scale (HOMS) asymptotic solution. Subsequently, the pointwise approximation properties of this solution to the original equations are analyzed, and its convergence rate in the integral norm is rigorously established under certain assumptions. Furthermore, a multiscale numerical algorithm is developed by integrating the finite element method (FEM), finite difference method, and interpolation technique. Finally, numerical experiments demonstrate the high accuracy, efficiency, and stability of the proposed HOMS numerical algorithm.
format Preprint
id arxiv_https___arxiv_org_abs_2604_05315
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Higher-Order Multiscale Computational Method for Multi-Continuum Problems in Highly Heterogeneous Media
Dong, Hao
Peng, Jiayuan
Huang, Jian
Numerical Analysis
Analysis of PDEs
This paper presents a high-accuracy higher-order multiscale method for solving multi-continuum problems in in highly heterogeneous media. First, microscopic unit cell functions are defined, leading to the derivation of macroscopic homogenized equations and formulas for calculating effective parameters, which yield a higher-order multi-scale (HOMS) asymptotic solution. Subsequently, the pointwise approximation properties of this solution to the original equations are analyzed, and its convergence rate in the integral norm is rigorously established under certain assumptions. Furthermore, a multiscale numerical algorithm is developed by integrating the finite element method (FEM), finite difference method, and interpolation technique. Finally, numerical experiments demonstrate the high accuracy, efficiency, and stability of the proposed HOMS numerical algorithm.
title Higher-Order Multiscale Computational Method for Multi-Continuum Problems in Highly Heterogeneous Media
topic Numerical Analysis
Analysis of PDEs
url https://arxiv.org/abs/2604.05315