Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems

DOI10.3934/dcdss.2015.8.119zbMath1302.65127OpenAlexW2006521263MaRDI QIDQ479074

Mario Ohlberger, Patrick Henning

Publication date: 5 December 2014

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2015.8.119

zbMATH Keywords

HMMmonotone operatormultiscale methodsa posteriori estimate

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Error analysis and interval analysis (65G99)

Related Items (12)

A multiscale model reduction method for nonlinear monotone elliptic equations in heterogeneous media ⋮ Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems ⋮ Adaptive heterogeneous multiscale methods for immiscible two-phase flow in porous media ⋮ Numerical Homogenization Methods for Parabolic Monotone Problems ⋮ An attempt at classifying homogenization-based numerical methods ⋮ A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities ⋮ High dimensional finite element method for multiscale nonlinear monotone parabolic equations ⋮ A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift ⋮ Preface: Homogenization-Based Numerical Methods ⋮ Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization ⋮ Heterogeneous Multiscale Method for the Maxwell equations with high contrast ⋮ Iterated Numerical Homogenization for MultiScale Elliptic Equations with Monotone Nonlinearity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Adaptive finite element heterogeneous multiscale method for homogenization problems
• The heterogeneous multiscale methods
• A posteriori error analysis of the heterogeneous multiscale method for homogenization problems
• Adaptive variational multiscale methods based on a posteriori error estimation: energy norm estimates for elliptic problems
• The heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains
• The variational multiscale method -- a paradigm for computational mechanics
• Hierarchical modeling of heterogeneous bodies
• Finite difference heterogeneous multi-scale method for homogenization problems.
• Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. I: Error estimates and adaptive algorithms
• The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift
• Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
• Multiscale finite element methods for nonlinear problems and their applications
• REDUCTION OF THE RESONANCE ERROR — PART 1: APPROXIMATION OF HOMOGENIZED COEFFICIENTS
• Analysis of the heterogeneous multiscale method for elliptic homogenization problems
• Analysis of the heterogeneous multiscale method for parabolic homogenization problems
• Numerical homogenization: survey, new results, and perspectives
• Multiscale Finite Element Methods
• An adaptive variational multiscale method for convection-diffusion problems
• A Framework for Adaptive Multiscale Methods for Elliptic Problems
• An Analytical Framework for Numerical Homogenization. Part II: Windowing and Oversampling
• Homogenization and Two-Scale Convergence
• Nichtlineare Funktionalanalysis
• Some Homogenization and Corrector Results for Nonlinear Monotone Operators
• Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces
• A Posteriori Error Estimates for the Heterogeneous Multiscale Finite Element Method for Elliptic Homogenization Problems
• The Heterogeneous Multi-Scale Method for Homogenization Problems
• An Analytical Framework for the Numerical Homogenization of Monotone Elliptic Operators and Quasiconvex Energies
• Reiterated homogenization of nonlinear monotone operators
• Estimation of local model error and goal-oriented adaptive modeling of heterogeneous materials. II: A computational environment for adaptive modeling of heterogeneous elastic solids

This page was built for publication: Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems