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Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media
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Estimation of Local Modeling Error and Goal-Oriented Adaptive Modeling of Heterogeneous Materials
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Correlation of Topographic Surface and Volume Data from Three-Dimensional Electron Microscopy
inferredcites →https://doi.org/10.1007/978-3-642-56205-1_4openalex-snapshot
Generalized FEM for Homogenization Problems
inferredcites →https://doi.org/10.1007/bfb0078314openalex-snapshot
Computation of oscillatory solutions to partial differential equations
inferredcites →https://doi.org/10.1007/pl00005409openalex-snapshot
Generalized p-FEM in homogenization
inferredcites →https://doi.org/10.1016/b978-0-12-068650-6.50020-4openalex-snapshot
THE COMBINED EFFECT OF CURVED BOUNDARIES AND NUMERICAL INTEGRATION IN ISOPARAMETRIC FINITE ELEMENT METHODS
inferredcites →https://doi.org/10.1016/s0021-9991(03)00303-6openalex-snapshot
Finite difference heterogeneous multi-scale method for homogenization problems
inferredcites →https://doi.org/10.1016/s0168-2024(08)x7014-6openalex-snapshot
The Finite Element Method for Elliptic Problems
inferredcites →https://doi.org/10.1016/s0169-7722(03)00065-2openalex-snapshot
Effects of pore volume–transmissivity correlation on transport phenomena
inferredcites →https://doi.org/10.1017/s0308210500027050openalex-snapshot
First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proof
inferredcites →https://doi.org/10.1061/(asce)0733-9399(2002)128:8(829)openalex-snapshot
Real Porous Media: Local Geometry and Transports
inferredcites →https://doi.org/10.1083/jcb.200202050openalex-snapshot
Phospholipids undergo hop diffusion in compartmentalized cell membrane
inferredcites →https://doi.org/10.1090/chel/374openalex-snapshot
Asymptotic Analysis for Periodic Structures
inferredcites →https://doi.org/10.1090/s0025-5718-99-01077-7openalex-snapshot
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
inferredcites →https://doi.org/10.1090/s0894-0347-04-00469-2openalex-snapshot
Analysis of the heterogeneous multiscale method for elliptic homogenization problems
inferredcites →https://doi.org/10.1093/oso/9780198565543.001.0001openalex-snapshot
An Introduction to Homogenization
inferredcites →https://doi.org/10.1103/physreve.59.4265openalex-snapshot
Percolation and conductivity of self-affine fractures
inferredcites →https://doi.org/10.1103/physrevlett.73.2382openalex-snapshot
Diffusion in the Presence of Topological Disorder
inferredcites →https://doi.org/10.1137/0153076openalex-snapshot
First-Order Corrections to the Homogenized Eigenvalues of a Periodic Composite Medium
inferredcites →https://doi.org/10.4310/cms.2003.v1.n1.a8openalex-snapshot
The Heterognous Multiscale Methods

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Impact of Numerical Methods in Thermal Modeling of Li‐Ion Batteries on Temperature Distribution and Computation Time
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A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method
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Solving Diffusion Problems on Rough Surfaces with a Hierarchical Multiscale FEM
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Multiscale Analysis and Modelling for Cancer Growth and Development
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Numerical Homogenization Methods for Parabolic Monotone Problems
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Heterogeneous Multiscale Methods with Quadrilateral Finite Elements
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Implementation of a Multiscale Method for Problems in Linear Elasticity
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The heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains
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A Multiscale Analysis of Diffusions on Rapidly Varying Surfaces
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A Multiscale Mathematical Model of Tumour Invasive Growth
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A short and versatile finite element multiscale code for homogenization problems
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Adaptive finite element heterogeneous multiscale method for homogenization problems
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Sparse tensor finite elements for elliptic multiple scale problems
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Adaptive reduced basis finite element heterogeneous multiscale method
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Multiscale methods for problems with complex geometry
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The heterogeneous multiscale finite element method for the homogenization of linear elastic solids and a comparison with the FE 2 method
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Deep CNNs as universal predictors of elasticity tensors in homogenization
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Multiscale method based on discontinuous Galerkin methods for homogenization problems
inferred← citeshttps://doi.org/10.1016/j.crma.2009.07.004openalex-snapshot
A posteriori error analysis of the heterogeneous multiscale method for homogenization problems
inferred← citeshttps://doi.org/10.1016/j.euromechsol.2019.02.001openalex-snapshot
Convergence and error analysis of FE-HMM/FE 2 for energetically consistent micro-coupling conditions in linear elastic solids
inferred← citeshttps://doi.org/10.1016/j.jcp.2011.03.001openalex-snapshot
A stochastic mixed finite element heterogeneous multiscale method for flow in porous media
inferred← citeshttps://doi.org/10.1016/j.jcp.2012.02.019openalex-snapshot
Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems
inferred← citeshttps://doi.org/10.1017/9781108594967openalex-snapshot
Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
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Preface
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Acknowledgements
inferred← citeshttps://doi.org/10.1017/9781108594967.003openalex-snapshot
Introduction
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Sobolev Space Basics
inferred← citeshttps://doi.org/10.1017/9781108594967.006openalex-snapshot
Optimal Recovery Splines
inferred← citeshttps://doi.org/10.1017/9781108594967.007openalex-snapshot
Numerical Homogenization
inferred← citeshttps://doi.org/10.1017/9781108594967.008openalex-snapshot
Operator-Adapted Wavelets
inferred← citeshttps://doi.org/10.1017/9781108594967.009openalex-snapshot
Fast Solvers
inferred← citeshttps://doi.org/10.1017/9781108594967.011openalex-snapshot
Gaussian Fields
inferred← citeshttps://doi.org/10.1017/9781108594967.012openalex-snapshot
Optimal Recovery Games on Hs0(Ω)
inferred← citeshttps://doi.org/10.1017/9781108594967.013openalex-snapshot
Gamblets
inferred← citeshttps://doi.org/10.1017/9781108594967.014openalex-snapshot
Hierarchical Games
inferred← citeshttps://doi.org/10.1017/9781108594967.016openalex-snapshot
Banach Space Basics
inferred← citeshttps://doi.org/10.1017/9781108594967.017openalex-snapshot
Optimal Recovery Splines
inferred← citeshttps://doi.org/10.1017/9781108594967.018openalex-snapshot
Gamblets
inferred← citeshttps://doi.org/10.1017/9781108594967.019openalex-snapshot
Bounded Condition Numbers
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Exponential Decay
inferred← citeshttps://doi.org/10.1017/9781108594967.021openalex-snapshot
Fast Gamblet Transform
inferred← citeshttps://doi.org/10.1017/9781108594967.023openalex-snapshot
Gaussian Measures, Cylinder Measures, and Fields on B
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Optimal Recovery Games on B
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Game Theoretic Interpretation of Gamblets
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Survey of Statistical Numerical Approximation
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Positive Definite Matrices
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Nonsymmetric Operators
inferred← citeshttps://doi.org/10.1017/9781108594967.030openalex-snapshot
Time-Dependent Operators
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Dense Kernel Matrices
inferred← citeshttps://doi.org/10.1017/9781108594967.033openalex-snapshot
Fundamental Concepts
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Bibliography
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Glossary
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Index
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Identities
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The heterogeneous multiscale method
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Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
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A two level approach for simulating Bose–Einstein condensates by Localized Orthogonal Decomposition
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The role of numerical integration in numerical homogenization
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Three-scale convergence for processes in heterogeneous media
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Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales
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Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
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Analysis of Eddy Currents in Rectangular Coils by Integral Equation Method in Sub-Domains
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Computation of effective resistivity in materials with microinclusions by a heterogeneous multiscale finite element method
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On A Priori Error Analysis of Fully Discrete Heterogeneous Multiscale FEM
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Convergence Analysis for The Numerical Boundary Corrector for Elliptic Equations with Rapidly Oscillating Coefficients
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Finite Element Heterogeneous Multiscale Methods with Near Optimal Computational Complexity
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Finite Element Heterogeneous Multiscale Method for the Wave Equation
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A Multiscale Moving Boundary Model Arising in Cancer Invasion
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Multilevel Monte Carlo Methods for Stochastic Elliptic Multiscale PDEs
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Finite Element Heterogeneous Multiscale Method for the Wave Equation: Long-Time Effects
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Bayesian Numerical Homogenization
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Multigrid with Rough Coefficients and Multiresolution Operator Decomposition from Hierarchical Information Games
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A Multiscale Finite Element Method for Oscillating Neumann Problem on Rough Domain
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Random Sampling and Efficient Algorithms for Multiscale PDEs
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Manifold Learning and Nonlinear Homogenization
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A Dilation-Based Seamless Multiscale Method for Elliptic Problems
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ANALYSIS OF A HETEROGENEOUS MULTISCALE FEM FOR PROBLEMS IN ELASTICITY
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COUPLING HETEROGENEOUS MULTISCALE FEM WITH RUNGE–KUTTA METHODS FOR PARABOLIC HOMOGENIZATION PROBLEMS: A FULLY DISCRETE SPACETIME ANALYSIS
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Simulations of (An)Isotropic Diffusion on Curved Biological Surfaces
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Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems
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Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
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A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift
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The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift
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Reactive Flow and Transport Through Complex Systems
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Multiscale Finite Element Methods for Flows on Rough Surfaces
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A Reduced Order Schwarz Method for Nonlinear Multiscale Elliptic Equations Based on Two-Layer Neural Networks
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Heterogeneous multiscale finite element method with novel numerical integration schemes
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Deep Convolutional Neural Networks Predict Elasticity Tensors and their Bounds in Homogenization
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Multi-scale Finite Element Method for incompressible flows in heterogeneous media : Implementation and Convergence analysis.
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