Multiscale asymptotic expansions and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients
type: Item
instance of: scholarly article
title: Multiscale asymptotic expansions and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients
zbMATH Open document ID: 1177.65147
published in: Applied Numerical Mathematics
publication date: 2009-10-09T00:00:00Z
review text: The authors discuss here the multiscale analysis and numerical algorithms for linear wave equations with rapidly oscillating coefficients which depend on spatial and temporal variables. The new contributions of the paper are a determination of the convergence rate under reasonable assumptions [cf. \textit{S. Brahim-Otsmane, G. A. Francfort} and \textit{F. Murat}, J. Math. Pures. Appl., IX. Sér. 71, No.~3, 197--231 (1992; Zbl 0837.35016)] higher-order correctors, and numerical approximations techniques. Some numerical results and unsolved problems are also presented.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35B27
zbMATH DE Number: 5611794
zbMATH Keywords: homogenization
zbMATH Keywords: multiscale asymptotic expansion
zbMATH Keywords: wave equation
zbMATH Keywords: rapidly oscillating coefficients
zbMATH Keywords: finite element method
zbMATH Keywords: symplectic geometric scheme
zbMATH Keywords: algorithms
zbMATH Keywords: convergence
zbMATH Keywords: numerical results
author: Qiao-Li Dong
author: Liqun Cao
MaRDI profile type: Publication
full work available at URL: j.apnum.2009.07.008
OpenAlex ID: W2011408025
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DOI: 10.1016/J.APNUM.2009.07.008
description: scientific article; zbMATH DE number 5611794