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On A Priori Error Analysis of Fully Discrete Heterogeneous Multiscale FEM

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inferredcites →https://doi.org/10.1006/jcph.2000.6585openalex-snapshot
Estimation of Local Modeling Error and Goal-Oriented Adaptive Modeling of Heterogeneous Materials
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inferredcites →https://doi.org/10.1007/978-3-642-56205-1_2openalex-snapshot
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inferredcites →https://doi.org/10.1016/s0168-2024(08)x7015-8openalex-snapshot
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inferredcites →https://doi.org/10.1090/chel/374openalex-snapshot
Asymptotic Analysis for Periodic Structures
inferredcites →https://doi.org/10.1090/s0025-5718-06-01909-0openalex-snapshot
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inferredcites →https://doi.org/10.1090/s0025-5718-99-01077-7openalex-snapshot
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inferredcites →https://doi.org/10.1090/s0894-0347-04-00469-2openalex-snapshot
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inferredcites →https://doi.org/10.1093/oso/9780198565543.001.0001openalex-snapshot
An Introduction to Homogenization
inferredcites →https://doi.org/10.1137/0153076openalex-snapshot
First-Order Corrections to the Homogenized Eigenvalues of a Periodic Composite Medium
inferredcites →https://doi.org/10.1137/030600771openalex-snapshot
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The Heterognous Multiscale Methods

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inferred← citeshttps://doi.org/10.1002/nme.4682openalex-snapshot
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inferred← citeshttps://doi.org/10.1002/nme.7565openalex-snapshot
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inferred← citeshttps://doi.org/10.1002/num.21769openalex-snapshot
A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method
inferred← citeshttps://doi.org/10.1007/11666806_6openalex-snapshot
Numerical Methods for Transport Problems in Microdevices
inferred← citeshttps://doi.org/10.1007/978-3-031-37981-9_5openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/978-3-319-10705-9_36openalex-snapshot
Multiscale Adaptive Method for Stokes Flow in Heterogenenous Media
inferred← citeshttps://doi.org/10.1007/978-3-319-10705-9_39openalex-snapshot
Reduced Basis Numerical Homogenization Method for the Multiscale Wave Equation
inferred← citeshttps://doi.org/10.1007/978-3-319-12316-5_10openalex-snapshot
Numerical Methods
inferred← citeshttps://doi.org/10.1007/978-3-319-41640-3_1openalex-snapshot
Numerical Homogenization Methods for Parabolic Monotone Problems
inferred← citeshttps://doi.org/10.1007/978-3-540-34288-5_72openalex-snapshot
Heterogeneous Multiscale Methods with Quadrilateral Finite Elements
inferred← citeshttps://doi.org/10.1007/978-3-540-70529-1_394openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s00030-017-0494-2openalex-snapshot
Sigma-convergence of semilinear stochastic wave equations
inferred← citeshttps://doi.org/10.1007/s00205-019-01400-wopenalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s00211-009-0244-4openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s00211-013-0578-9openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s00211-015-0703-zopenalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s00466-025-02694-2openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s10208-015-9246-zopenalex-snapshot
Reduction in the Resonance Error in Numerical Homogenization II: Correctors and Extrapolation
inferred← citeshttps://doi.org/10.1007/s10596-014-9455-6openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s10915-022-01834-7openalex-snapshot
Multiscale Finite Element Methods for an Elliptic Optimal Control Problem with Rough Coefficients
inferred← citeshttps://doi.org/10.1016/j.cam.2015.05.012openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.cam.2017.06.029openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.cam.2020.112960openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.cam.2021.113873openalex-snapshot
Analysis of non-local multicontinuum upscaling for dual continuum model
inferred← citeshttps://doi.org/10.1016/j.camwa.2020.06.007openalex-snapshot
The Dune framework: Basic concepts and recent developments
inferred← citeshttps://doi.org/10.1016/j.cma.2009.03.019openalex-snapshot
A short and versatile finite element multiscale code for homogenization problems
inferred← citeshttps://doi.org/10.1016/j.cma.2010.06.012openalex-snapshot
Adaptive finite element heterogeneous multiscale method for homogenization problems
inferred← citeshttps://doi.org/10.1016/j.cma.2013.01.002openalex-snapshot
Adaptive reduced basis finite element heterogeneous multiscale method
inferred← citeshttps://doi.org/10.1016/j.cma.2017.10.001openalex-snapshot
The heterogeneous multiscale finite element method for the homogenization of linear elastic solids and a comparison with the FE 2 method
inferred← citeshttps://doi.org/10.1016/j.commatsci.2012.06.012openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.crma.2007.11.029openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.crma.2009.07.004openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.crma.2011.09.005openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.crma.2013.06.002openalex-snapshot
FE heterogeneous multiscale method for long-time wave propagation
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.2008.04.037openalex-snapshot
Upscaling methods for a class of convection–diffusion equations with highly oscillating coefficients
inferred← citeshttps://doi.org/10.1016/j.jcp.2011.03.001openalex-snapshot
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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/10.1016/j.jcp.2015.04.016openalex-snapshot
A reduced basis localized orthogonal decomposition
inferred← citeshttps://doi.org/10.1016/j.jcp.2016.03.009openalex-snapshot
A time dependent approach for removing the cell boundary error in elliptic homogenization problems
inferred← citeshttps://doi.org/10.1016/j.paerosci.2011.05.001openalex-snapshot
Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles
inferred← citeshttps://doi.org/10.1016/j.procs.2013.05.268openalex-snapshot
A Multiscale Model for Aberrant Crypt Foci
inferred← citeshttps://doi.org/10.1017/s0962492912000025openalex-snapshot
The heterogeneous multiscale method
inferred← citeshttps://doi.org/10.1051/m2an/2018064openalex-snapshot
Heterogeneous Multiscale Method for the Maxwell equations with high contrast
inferred← citeshttps://doi.org/10.1051/m2an/2019093openalex-snapshot
Finite element approximation of elliptic homogenization problems in nondivergence-form
inferred← citeshttps://doi.org/10.1051/m2an/2024040openalex-snapshot
A two level approach for simulating Bose–Einstein condensates by Localized Orthogonal Decomposition
inferred← citeshttps://doi.org/10.1051/proc/201237002openalex-snapshot
Numerical homogenization: survey, new results, and perspectives
inferred← citeshttps://doi.org/10.1051/proc/201550001openalex-snapshot
The role of numerical integration in numerical homogenization
inferred← citeshttps://doi.org/10.1080/00036811.2011.569498openalex-snapshot
Three-scale convergence for processes in heterogeneous media
inferred← citeshttps://doi.org/10.1080/15502287.2016.1145761openalex-snapshot
A Large Strains Finite Element Multiscale Approach
inferred← citeshttps://doi.org/10.1090/mcom/3114openalex-snapshot
Localized orthogonal decomposition method for the wave equation with a continuum of scales
inferred← citeshttps://doi.org/10.1090/s0025-5718-2011-02527-5openalex-snapshot
Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales
inferred← citeshttps://doi.org/10.1090/s0025-5718-2013-02758-5openalex-snapshot
Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
inferred← citeshttps://doi.org/10.1093/imanum/drt066openalex-snapshot
Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales
inferred← citeshttps://doi.org/10.1093/imanum/dru010openalex-snapshot
Random walk in random environment, corrector equation and homogenized coefficients: from theory to numerics, back and forth
inferred← citeshttps://doi.org/10.1098/rsta.2013.0388openalex-snapshot
Reduced-order modelling numerical homogenization
inferred← citeshttps://doi.org/10.1109/apeie59731.2023.10347576openalex-snapshot
Retrieving Rock Conductivity Model During Well Drilling
inferred← citeshttps://doi.org/10.1134/s1029959917040051openalex-snapshot
Computation of effective resistivity in materials with microinclusions by a heterogeneous multiscale finite element method
inferred← citeshttps://doi.org/10.1137/040612622openalex-snapshot
The Heterogeneous Multiscale Method Based on the Discontinuous Galerkin Method for Hyperbolic and Parabolic Problems
inferred← citeshttps://doi.org/10.1137/060649112openalex-snapshot
An Analytical Framework for the Numerical Homogenization of Monotone Elliptic Operators and Quasiconvex Energies
inferred← citeshttps://doi.org/10.1137/060676118openalex-snapshot
Finite Element Heterogeneous Multiscale Methods with Near Optimal Computational Complexity
inferred← citeshttps://doi.org/10.1137/100800488openalex-snapshot
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inferred← citeshttps://doi.org/10.1137/110836626openalex-snapshot
An Efficient High Order Heterogeneous Multiscale Method for Elliptic Problems
inferred← citeshttps://doi.org/10.1137/120885541openalex-snapshot
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inferred← citeshttps://doi.org/10.1137/120894725openalex-snapshot
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inferred← citeshttps://doi.org/10.1137/130933198openalex-snapshot
Localized Orthogonal Decomposition Techniques for Boundary Value Problems
inferred← citeshttps://doi.org/10.1137/13094195xopenalex-snapshot
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inferred← citeshttps://doi.org/10.1137/130950136openalex-snapshot
An Adaptive Finite Element Heterogeneous Multiscale Method for Stokes Flow in Porous Media
inferred← citeshttps://doi.org/10.1137/140975504openalex-snapshot
Linearized Numerical Homogenization Method for Nonlinear Monotone Parabolic Multiscale Problems
inferred← citeshttps://doi.org/10.1137/15m1025633openalex-snapshot
A Priori Error Analysis of the Finite Element Heterogeneous Multiscale Method for the Wave Equation over Long Time
inferred← citeshttps://doi.org/10.1137/15m1039225openalex-snapshot
A New Heterogeneous Multiscale Method for Time-Harmonic Maxwell's Equations
inferred← citeshttps://doi.org/10.1137/15m105389xopenalex-snapshot
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inferred← citeshttps://doi.org/10.1137/16m1074436openalex-snapshot
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inferred← citeshttps://doi.org/10.1137/16m1091320openalex-snapshot
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inferred← citeshttps://doi.org/10.1137/16m1108820openalex-snapshot
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inferred← citeshttps://doi.org/10.1137/18m1187891openalex-snapshot
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inferred← citeshttps://doi.org/10.1137/18m1234072openalex-snapshot
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inferred← citeshttps://doi.org/10.1137/20m1363832openalex-snapshot
Explicit and Energy-Conserving Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method for Wave Propagation in Heterogeneous Media
inferred← citeshttps://doi.org/10.1137/21m1402625openalex-snapshot
Online Adaptive Algorithm for Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method
inferred← citeshttps://doi.org/10.1137/21m1443960openalex-snapshot
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inferred← citeshttps://doi.org/10.1137/21m1452123openalex-snapshot
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inferred← citeshttps://doi.org/10.1137/23m1596272openalex-snapshot
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inferred← citeshttps://doi.org/10.1137/24m1686218openalex-snapshot
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inferred← citeshttps://doi.org/10.1142/9789814366892_0009openalex-snapshot
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inferred← citeshttps://doi.org/10.1142/s0218202506001285openalex-snapshot
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inferred← citeshttps://doi.org/10.1142/s0218202512500029openalex-snapshot
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inferred← citeshttps://doi.org/10.1142/s0218202521500603openalex-snapshot
A parabolic local problem with exponential decay of the resonance error for numerical homogenization
inferred← citeshttps://doi.org/10.1186/s40323-015-0052-6openalex-snapshot
Effect of the separated approximation of input data in the accuracy of the resulting PGD solution
inferred← citeshttps://doi.org/10.1186/s40687-017-0118-9openalex-snapshot
On heterogeneous coupling of multiscale methods for problems with and without scale separation
inferred← citeshttps://doi.org/10.1515/9783110671490-006openalex-snapshot
6 Localized model reduction for parameterized problems
inferred← citeshttps://doi.org/10.1515/jnma-2014-0074openalex-snapshot
Duality-based adaptivity in finite element discretization of heterogeneous multiscale problems
inferred← citeshttps://doi.org/10.1553/etna_vol54s234openalex-snapshot
Additive Schwarz preconditioners for a localized orthogonal decomposition method
inferred← citeshttps://doi.org/10.1615/intjmultcompeng.2014007470openalex-snapshot
A MULTISCALE COMPUTATIONAL METHOD FOR 2D ELASTOPLASTIC DYNAMIC ANALYSIS OF HETEROGENEOUS MATERIALS
inferred← citeshttps://doi.org/10.3934/dcdss.2015.8.91openalex-snapshot
Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
inferred← citeshttps://doi.org/10.3934/dcdss.2016056openalex-snapshot
A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift
inferred← citeshttps://doi.org/10.3934/nhm.2010.5.711openalex-snapshot
The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift
inferred← citeshttps://doi.org/10.3934/nhm.2012.7.503openalex-snapshot
Convergence of MsFEM approximations for elliptic, non-periodic homogenization problems
inferred← citeshttps://doi.org/10.3934/nhm.2020002openalex-snapshot
Mathematical analysis of transmission properties of electromagnetic meta-materials
inferred← citeshttps://doi.org/10.3934/proc.2005.2005.11openalex-snapshot
Multiscale methods for advection-diffusion problems
inferred← citeshttps://doi.org/10.4171/owr/2005/49openalex-snapshot
Reactive Flow and Transport Through Complex Systems
inferred← citeshttps://doi.org/10.4171/owr/2011/16openalex-snapshot
Geometric Numerical Integration
inferred← citeshttps://doi.org/10.4171/owr/2015/2openalex-snapshot
New Discretization Methods for the Numerical Approximation of PDEs
inferred← citeshttps://doi.org/10.4208/cicp.2007.v2.p367openalex-snapshot
Heterogeneous Multiscale Methods: A Review
inferred← citeshttps://doi.org/10.4208/jcm.1703-m2015-0433openalex-snapshot
Heterogeneous Multiscale Method for Optimal Control Problem Governed by Elliptic Equations with Highly Oscillatory Coefficients
inferred← citeshttps://doi.org/10.4310/cms.2010.v8.n4.a4openalex-snapshot
Heterogeneous multiscale finite element method with novel numerical integration schemes
inferred← citeshttps://doi.org/10.4310/cms.2016.v14.n2.a7openalex-snapshot
A finite element heterogeneous multiscale method with improved control over the modeling error
inferred← citeshttps://doi.org/10.4310/cms.2018.v16.n8.a11openalex-snapshot
An equation-free approach for second order multiscale hyperbolic problems in non-divergence form
inferred← citeshttps://doi.org/10.48550/arxiv.1908.02074openalex-snapshot
Towards Automatic and Reliable Localized Model Order Reduction
inferred← citeshttps://doi.org/10.5445/ir/1000138844openalex-snapshot
The heterogeneous multiscale method for dispersive Maxwell systems
inferred← citeshttps://doi.org/10.5451/unibas-006145369openalex-snapshot
Finite element heterogeneous multiscale methods for the wave equation
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