L2-GLOBAL TO LOCAL PROJECTION: AN APPROACH TO MULTISCALE ANALYSIS

DOI10.1142/S0218202511005714zbMath1242.65234OpenAlexW2003171158MaRDI QIDQ2883364

Ivo M. Babuška, Robert P. Lipton

Publication date: 10 May 2012

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202511005714

zbMATH Keywords

homogenizationerror analysismultiscale analysisgradient fieldsglobal-local methodheterogenous media\(L_2\)-projection

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element methods applied to problems in solid mechanics (74S05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Homogenization in equilibrium problems of solid mechanics (74Q05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (11)

A time dependent approach for removing the cell boundary error in elliptic homogenization problems ⋮ An Optimization Based Coupling Method for Multiscale Problems ⋮ A Nitsche hybrid multiscale method with non-matching grids ⋮ A reduced basis localized orthogonal decomposition ⋮ A stochastic multiscale method for the elastodynamic wave equation arising from fiber composites ⋮ A concurrent global-local numerical method for multiscale PDEs ⋮ A fuzzy-stochastic multiscale model for fiber composites, a one-dimensional study ⋮ Bridging multiple structural scales with a generalized finite element method ⋮ Analysis and improvements of global-local enrichments for the generalized finite element method ⋮ Reduction in the resonance error in numerical homogenization. II: Correctors and extrapolation ⋮ On heterogeneous coupling of multiscale methods for problems with and without scale separation

Cites Work

• Unnamed Item
• Unnamed Item
• The penetration function and its application to microscale problems
• Composites with a periodic structure: Mathematical analysis and numerical treatment
• A variational approach to the theory of the elastic behaviour of multiphase materials
• Non-homogeneous media and vibration theory
• A multiscale finite element method for elliptic problems in composite materials and porous media
• The partition of unity finite element method: basic theory and applications
• Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. I: Error estimates and adaptive algorithms
• Periodic unfolding and homogenization
• Damage analysis of fiber composites. I: Statistical analysis of fiber scale
• Bounds on the distribution of extreme values for the stress in composite materials
• Numerical methods for multiscale elliptic problems
• Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems
• p-version of the generalized FEM using mesh-based handbooks with applications to multiscale problems
• A Framework for Adaptive Multiscale Methods for Elliptic Problems
• Convergence Analysis for The Numerical Boundary Corrector for Elliptic Equations with Rapidly Oscillating Coefficients
• A Projection Method Applied to Diffusion in a Periodic Structure
• Homogenization and Two-Scale Convergence
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients
• THE PARTITION OF UNITY METHOD
• First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proof
• Homogenization of Periodic Structures via Bloch Decomposition
• Numerical Homogenization of Nonlinear Random Parabolic Operators
• Assessment of the local stress state through macroscopic variables
• Homogenization and Field Concentrations in Heterogeneous Media
• Viscoelastic fiber reinforced materials.
• Global‐local finite element
• GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE

This page was built for publication: L²-GLOBAL TO LOCAL PROJECTION: AN APPROACH TO MULTISCALE ANALYSIS