A multiscale model reduction method for nonlinear monotone elliptic equations in heterogeneous media
From MaRDI portal
Publication:1679921
DOI10.3934/nhm.2017025zbMath1377.65148OpenAlexW2764051196MaRDI QIDQ1679921
Eric T. Chung, Ke Shi, Shuai Ye, Yalchin R. Efendiev
Publication date: 22 November 2017
Published in: Networks and Heterogeneous Media (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/nhm.2017025
convergence\(p\)-Laplacianmultiscalenumerical resultgeneralized multiscale finite element methodhigh-contrastnonlinear monotone elliptic problem
Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Quasilinear elliptic equations with (p)-Laplacian (35J92)
Related Items (8)
Generalized multiscale hybridizable discontinuous Galerkin (GMsHDG) method for flows in nonlinear porous media ⋮ A Reduced Order Schwarz Method for Nonlinear Multiscale Elliptic Equations Based on Two-Layer Neural Networks ⋮ A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales ⋮ Adaptive multiscale model reduction with generalized multiscale finite element methods ⋮ High dimensional finite element method for multiscale nonlinear monotone parabolic equations ⋮ Generalized multiscale finite element method for a strain-limiting nonlinear elasticity model ⋮ Analysis on an HDG method for the \(p\)-Laplacian equations ⋮ 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
- Unnamed Item
- Unnamed Item
- Generalized multiscale finite element methods (GMsFEM)
- Multiscale empirical interpolation for solving nonlinear PDEs
- Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems
- Multiscale finite element methods for high-contrast problems using local spectral basis functions
- Flux norm approach to finite-dimensional homogenization approximations with non-separated scales and high contrast
- Reduced-order multiscale modeling of nonlinear \(p\)-Laplacian flows in high-contrast media
- An adaptive GMsFEM for high-contrast flow problems
- The heterogeneous multiscale methods
- Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows
- The variational multiscale method -- a paradigm for computational mechanics
- Analysis of upscaling absolute permeability
- A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- Residual-driven online generalized multiscale finite element methods
- 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
- Randomized Oversampling for Generalized Multiscale Finite Element Methods
- Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
- A Multiscale Enrichment Procedure for Nonlinear Monotone Operators
- Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
- Coarse-Grid Multiscale Model Reduction Techniques for Flows in Heterogeneous Media and Applications
- Domain Decomposition Preconditioners for Multiscale Flows in High-Contrast Media
- Domain Decomposition Preconditioners for Multiscale Flows in High Contrast Media: Reduced Dimension Coarse Spaces
- Analysis of the heterogeneous multiscale method for elliptic homogenization problems
- A new multiscale finite element method for high-contrast elliptic interface problems
- Homogenization of monotone operators
- Multiscale Finite Element Methods
- Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
- Homogenization and Two-Scale Convergence
- Analysis of a Two-Scale, Locally Conservative Subgrid Upscaling for Elliptic Problems
- Error of the Network Approximation for Densely Packed Composites with Irregular Geometry
- Numerical Homogenization and Correctors for Nonlinear Elliptic Equations
- Robust Multiscale Iterative Solvers for Nonlinear Flows in Highly Heterogeneous Media
- Variational Multiscale Analysis: the Fine‐scale Green’s Function, Projection, Optimization, Localization, and Stabilized Methods
- The Staggered DG Method is the Limit of a Hybridizable DG Method
- A Multiscale Finite Element Method for Numerical Homogenization
- Discrete Network Approximation for Highly-Packed Composites with Irregular Geometry in Three Dimensions
- Reiterated homogenization of nonlinear monotone operators
This page was built for publication: A multiscale model reduction method for nonlinear monotone elliptic equations in heterogeneous media
