A Priori Error Analysis of the Finite Element Heterogeneous Multiscale Method for the Wave Equation over Long Time

DOI10.1137/15M1025633zbMath1382.65303OpenAlexW1623422195MaRDI QIDQ2807287

Timothée Pouchon, Assyr Abdulle

Publication date: 20 May 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1025633

zbMATH Keywords

wave equationheterogeneous mediadispersive wavesmultiscale methodlong time behaviora priori error analysiseffective equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Periodic solutions to PDEs (35B10) Effective constitutive equations in solid mechanics (74Q15) Wave equation (35L05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Homogenization and oscillations in dynamical problems of solid mechanics (74Q10)

Related Items (12)

Optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures ⋮ Effective models and numerical homogenization for wave propagation in heterogeneous media on arbitrary timescales ⋮ Numerical homogenization beyond scale separation ⋮ A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures ⋮ Crime pays; homogenized wave equations for long times ⋮ A homogenized model accounting for dispersion, interfaces and source points for transient waves in 1D periodic media ⋮ Numerical multiscale methods for waves in high-contrast media ⋮ Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization ⋮ Finite element approximation of elliptic homogenization problems in nondivergence-form ⋮ Effective Models for Long Time Wave Propagation in Locally Periodic Media ⋮ Finite element heterogeneous multiscale method for elastic waves in heterogeneous media ⋮ High-order homogenization in optimal control by the Bloch wave method

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