CONSTRAINT ENERGY MINIMIZING GENERALIZED MULTISCALE FINITE ELEMENT METHOD FOR CONVECTION DIFFUSION EQUATION

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Original languageEnglish
Pages (from-to)735-752
Journal / PublicationMultiscale Modeling and Simulation
Volume21
Issue number2
Online published5 Jun 2023
Publication statusPublished - 2023

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Abstract

In this paper we present and analyze a constraint energy minimizing generalized multiscale finite element method for convection diffusion equations. To define the multiscale basis functions, we first build an auxiliary multiscale space by solving local spectral problems motivated by analysis. Then a constraint energy minimization performed in the oversampling domains is exploited to construct the multiscale space. The resulting multiscale basis functions have a good decay property even for high contrast diffusion and convection coefficients. Furthermore, if the number of oversampling layers is chosen properly, we can prove that the convergence rate is proportional to the coarse meshsize. Our analysis also indicates that the size of the oversampling domain weakly depends on the contrast of the heterogeneous coefficients. Several numerical experiments are presented illustrating the performance of our method. © 2023 Society for Industrial and Applied Mathematics Publications. All rights reserved.

Research Area(s)

  • convection diffusion equation, local multiscale basis function, local spectral problem, multiscale method

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