Reduction in the resonance error in numerical homogenization. II: Correctors and extrapolation
From MaRDI portal
Publication:5963084
DOI10.1007/s10208-015-9246-zzbMath1335.65086arXiv1409.1155OpenAlexW2039055469MaRDI QIDQ5963084
Antoine Gloria, Zakaria Habibi
Publication date: 4 March 2016
Published in: Foundations of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1409.1155
randomnumerical experimentsalmost periodiccorrectorseffective coefficientsergodic coefficientsnumerical homogenizationperiodicPoisson random inclusionsresonance error
Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)
Related Items (16)
Bloch wave approach to almost periodic homogenization and approximations of effective coefficients ⋮ A time dependent approach for removing the cell boundary error in elliptic homogenization problems ⋮ Numerical homogenization: survey, new results, and perspectives ⋮ Bloch wave homogenisation of quasiperiodic media ⋮ A Nitsche hybrid multiscale method with non-matching grids ⋮ Local Profiles for Elliptic Problems at Different Scales: Defects in, and Interfaces between Periodic Structures ⋮ A short proof of Gevrey regularity for homogenized coefficients of the Poisson point process ⋮ Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields ⋮ An Elliptic Local Problem with Exponential Decay of the Resonance Error for Numerical Homogenization ⋮ Numerical upscaling via the wave equation with perfectly matched layers ⋮ Efficient methods for the estimation of homogenized coefficients ⋮ Computing homogenized coefficientsviamultiscale representation and hierarchical hybrid grids ⋮ A regularity theory for random elliptic operators ⋮ Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues ⋮ A parabolic local problem with exponential decay of the resonance error for numerical homogenization ⋮ Analyticity of homogenized coefficients under Bernoulli perturbations and the Clausius-Mossotti formulas
Cites Work
- Structural optimization with FreeFem++
- Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation
- A multiscale finite element method for elliptic problems in composite materials and porous media
- Quantitative results on the corrector equation in stochastic homogenization
- Spectral measure and approximation of homogenized coefficients
- Improving on computation of homogenized coefficients in the periodic and quasi-periodic settings
- Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics
- Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations
- An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations
- Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
- L2-GLOBAL TO LOCAL PROJECTION: AN APPROACH TO MULTISCALE ANALYSIS
- Localized Bases for Finite-Dimensional Homogenization Approximations with Nonseparated Scales and High Contrast
- REDUCTION OF THE RESONANCE ERROR — PART 1: APPROXIMATION OF HOMOGENIZED COEFFICIENTS
- Analysis of the heterogeneous multiscale method for elliptic homogenization problems
- Metric-based upscaling
- Numerical homogenization: survey, new results, and perspectives
- An Analytical Framework for Numerical Homogenization. Part II: Windowing and Oversampling
- A homogenization result for planar, polygonal networks
- Homogenization and Two-Scale Convergence
- Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
- Convergence of a Nonconforming Multiscale Finite Element Method
- Random walk in random environment, corrector equation and homogenized coefficients: from theory to numerics, back and forth
- Oversampling for the Multiscale Finite Element Method
- On A Priori Error Analysis of Fully Discrete Heterogeneous Multiscale FEM
- A Multiscale Finite Element Method for Numerical Homogenization
- An Analytical Framework for the Numerical Homogenization of Monotone Elliptic Operators and Quasiconvex Energies
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Reduction in the resonance error in numerical homogenization. II: Correctors and extrapolation
