Multiscale asymptotic expansions and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients

DOI10.1016/j.apnum.2009.07.008zbMath1177.65147OpenAlexW2011408025MaRDI QIDQ731967

Li-qun Cao, Qiao-Li Dong

Publication date: 9 October 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2009.07.008

zbMATH Keywords

algorithmsconvergencenumerical resultswave equationfinite element methodhomogenizationmultiscale asymptotic expansionrapidly oscillating coefficientssymplectic geometric scheme

Mathematics Subject Classification ID

Wave equation (35L05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

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Cites Work

• The heterogeneous multiscale methods
• Non-homogeneous media and vibration theory
• Symplectic schemes for nonautonomous Hamiltonian system
• Homogenization of reticulated structures
• Asymptotic expansions and numerical algorithms of eigenvalues and eigenfunctions of the Dirichlet problem for second order elliptic equations in perforated domains
• Correctors for the homogenization of the wave and heat equations
• Homogenization and porous media
• Multiscale asymptotic expansion and finite element methods for the mixed boundary value problems of second order elliptic equation in perforated domains
• Homogenization of the Schrödinger equation and effective mass theorems
• Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
• Analysis of a Two-Scale, Locally Conservative Subgrid Upscaling for Elliptic Problems
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