On the public citation graph

A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method

https://doi.org/10.1002/num.21769
0 signed · 75 inferred · view as graph

Inferred edges come from two machine sources: sweeps of open repository metadata (mostly SSRN and Zenodo), and a bulk OpenAlex citation snapshot. Every row below is labelled with the one it came from. Neither is a complete citation index — absence here is not evidence of absence.

Is this your work? Sign in with ORCID and put your name on the claims that are yours.
Claim with ORCID
Reference health. See whether every reference in this work resolves to a known work and none has been retracted — and get a dated CiteStamped badge you can embed.
See reference health

What this work says

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

inferredcites →https://doi.org/10.1002/nme.3276openalex-snapshot
Guaranteed computable bounds on quantities of interest in finite element computations
inferredcites →https://doi.org/10.1007/3-540-26444-2_9openalex-snapshot
Adaptive Variational Multiscale Methods Based on A Posteriori Error Estimation: Duality Techniques for Elliptic Problems
inferredcites →https://doi.org/10.1007/978-0-387-09496-0openalex-snapshot
Multiscale Finite Element Methods: Theory and Applications
inferredcites →https://doi.org/10.1007/978-1-4615-9966-1openalex-snapshot
Partial Differential Equations
inferredcites →https://doi.org/10.1007/978-1-4757-4317-3openalex-snapshot
The Boundary Value Problems of Mathematical Physics
inferredcites →https://doi.org/10.1007/978-3-0348-7605-6openalex-snapshot
Adaptive Finite Element Methods for Differential Equations
inferredcites →https://doi.org/10.1007/978-3-540-34288-5_72openalex-snapshot
Heterogeneous Multiscale Methods with Quadrilateral Finite Elements
inferredcites →https://doi.org/10.1007/978-3-642-84659-5openalex-snapshot
Homogenization of Differential Operators and Integral Functionals
inferredcites →https://doi.org/10.1007/978-3-662-09021-3openalex-snapshot
Numerische Mathematik 1
inferredcites →https://doi.org/10.1007/bf01397880openalex-snapshot
On cubature formulae with a minimal number of knots
inferredcites →https://doi.org/10.1007/pl00005409openalex-snapshot
Generalized p-FEM in homogenization
inferredcites →https://doi.org/10.1007/s00211-010-0335-2openalex-snapshot
The effect of numerical integration on the finite element approximation of linear functionals
inferredcites →https://doi.org/10.1016/0045-7825(95)00844-9openalex-snapshot
Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
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/c2013-0-10319-4openalex-snapshot
The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations
inferredcites →https://doi.org/10.1016/j.cam.2005.04.032openalex-snapshot
P2Q2Iso2D=2D Isoparametric FEM in Matlab
inferredcites →https://doi.org/10.1016/j.cma.2006.08.019openalex-snapshot
Adaptive variational multiscale methods based on a posteriori error estimation: Energy norm estimates for elliptic problems
inferredcites →https://doi.org/10.1016/j.cma.2009.03.019openalex-snapshot
A short and versatile finite element multiscale code for homogenization problems
inferredcites →https://doi.org/10.1016/j.cma.2010.06.012openalex-snapshot
Adaptive finite element heterogeneous multiscale method for homogenization problems
inferredcites →https://doi.org/10.1016/j.cma.2013.01.002openalex-snapshot
Adaptive reduced basis finite element heterogeneous multiscale method
inferredcites →https://doi.org/10.1016/j.commatsci.2012.06.012openalex-snapshot
Multiscale modeling of residual stresses in isotropic conductive adhesives with nano-particles
inferredcites →https://doi.org/10.1016/j.crma.2007.11.029openalex-snapshot
Multiscale method based on discontinuous Galerkin methods for homogenization problems
inferredcites →https://doi.org/10.1016/j.crma.2009.07.004openalex-snapshot
A posteriori error analysis of the heterogeneous multiscale method for homogenization problems
inferredcites →https://doi.org/10.1016/j.jcp.2011.03.001openalex-snapshot
A stochastic mixed finite element heterogeneous multiscale method for flow in porous media
inferredcites →https://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
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/s0045-7825(96)01107-3openalex-snapshot
A posteriori error estimation in finite element analysis
inferredcites →https://doi.org/10.1016/s0045-7825(98)00079-6openalex-snapshot
The variational multiscale method—a paradigm for computational mechanics
inferredcites →https://doi.org/10.1016/s0045-7825(98)00343-0openalex-snapshot
On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors
inferredcites →https://doi.org/10.1016/s0898-1221(00)00317-5openalex-snapshot
Goal-oriented error estimation and adaptivity for the finite element method
inferredcites →https://doi.org/10.1017/s0962492900002701openalex-snapshot
Constructing cubature formulae: the science behind the art
inferredcites →https://doi.org/10.1017/s0962492901000010openalex-snapshot
An optimal control approach to a posteriori error estimation in finite element methods
inferredcites →https://doi.org/10.1017/s096249290200003xopenalex-snapshot
Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
inferredcites →https://doi.org/10.1017/s0962492912000025openalex-snapshot
The heterogeneous multiscale method
inferredcites →https://doi.org/10.1090/s0025-5718-04-01757-0openalex-snapshot
Book Review: Report on global methods for combinatorial isoperimetric problems
inferredcites →https://doi.org/10.1090/s0025-5718-2011-02527-5openalex-snapshot
Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales
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/comjnl/17.4.370openalex-snapshot
Topics in Numerical Analysis
inferredcites →https://doi.org/10.1093/imanum/drm026openalex-snapshot
A safeguarded dual weighted residual method
inferredcites →https://doi.org/10.1093/oso/9780198502760.001.0001openalex-snapshot
The Finite Element Method and its Reliability
inferredcites →https://doi.org/10.1103/physrevb.67.092101openalex-snapshot
Heterogeneous multiscale method: A general methodology for multiscale modeling
inferredcites →https://doi.org/10.1109/mcse.1999.10004openalex-snapshot
Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics
inferredcites →https://doi.org/10.1115/1.3424588openalex-snapshot
Asymptotic Analysis of Periodic Structures
inferredcites →https://doi.org/10.1137/030600771openalex-snapshot
Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces
inferredcites →https://doi.org/10.1137/030601077openalex-snapshot
High-Dimensional Finite Elements for Elliptic Problems with Multiple Scales
inferredcites →https://doi.org/10.1137/040605229openalex-snapshot
A Posteriori Error Estimates for the Heterogeneous Multiscale Finite Element Method for Elliptic Homogenization Problems
inferredcites →https://doi.org/10.1137/040607137openalex-snapshot
On A Priori Error Analysis of Fully Discrete Heterogeneous Multiscale FEM
inferredcites →https://doi.org/10.1137/050632488openalex-snapshot
MultiScale Modeling of Physical Phenomena: Adaptive Control of Models
inferredcites →https://doi.org/10.1137/0520043openalex-snapshot
A General Convergence Result for a Functional Related to the Theory of Homogenization
inferredcites →https://doi.org/10.1137/060676118openalex-snapshot
Finite Element Heterogeneous Multiscale Methods with Near Optimal Computational Complexity
inferredcites →https://doi.org/10.1137/070693230openalex-snapshot
A Framework for Adaptive Multiscale Methods for Elliptic Problems
inferredcites →https://doi.org/10.1137/0715049openalex-snapshot
Error Estimates for Adaptive Finite Element Computations
inferredcites →https://doi.org/10.1137/0720034openalex-snapshot
Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods
inferredcites →https://doi.org/10.1137/0731051openalex-snapshot
Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients
inferredcites →https://doi.org/10.1142/9789814366892_0009openalex-snapshot
A Priori and a Posteriori Error Analysis for Numerical Homogenization: A Unified Framework
inferredcites →https://doi.org/10.1142/s0218202506001285openalex-snapshot
ANALYSIS OF A HETEROGENEOUS MULTISCALE FEM FOR PROBLEMS IN ELASTICITY
inferredcites →https://doi.org/10.1142/s0218202511005507openalex-snapshot
REDUCTION OF THE RESONANCE ERROR — PART 1: APPROXIMATION OF HOMOGENIZED COEFFICIENTS
inferredcites →https://doi.org/10.4310/cms.2003.v1.n1.a8openalex-snapshot
The Heterognous Multiscale Methods
inferredcites →https://doi.org/10.5075/epfl-thesis-5097openalex-snapshot
Adaptive Finite Element Methods for Multiscale Partial Differential Equations

What points at this work

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

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/s00466-021-01990-xopenalex-snapshot
Goal-oriented error estimation and adaptivity in MsFEM computations
inferred← citeshttps://doi.org/10.1007/s10444-020-09833-8openalex-snapshot
An adaptive multiscale hybrid-mixed method for the Oseen equations
inferred← citeshttps://doi.org/10.1007/s10915-016-0338-yopenalex-snapshot
A Goal-Oriented Error Estimator for a Class of Homogenization Problems
inferred← citeshttps://doi.org/10.1016/j.apm.2025.116673openalex-snapshot
A variational multiscale approach to goal-oriented error estimation in finite element analysis of convection-diffusion-reaction problems
inferred← citeshttps://doi.org/10.1016/j.apm.2026.117280openalex-snapshot
Similarity-informed active learning method for efficient multiscale analysis of conformal lattice structures
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.2016.03.016openalex-snapshot
A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media
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/10.1017/s0962492912000025openalex-snapshot
The heterogeneous multiscale method
inferred← citeshttps://doi.org/10.1093/imanum/drz053openalex-snapshot
On a multiscalea posteriorierror estimator for the stokes and Brinkman equations
inferred← citeshttps://doi.org/10.1098/rsta.2013.0377openalex-snapshot
Multiscale modelling and simulation: a position paper
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/10.1137/16m1105670openalex-snapshot
A Duality-Based Optimization Approach for Model Adaptivity in Heterogeneous Multiscale Problems
inferred← citeshttps://doi.org/10.1515/jnma-2014-0074openalex-snapshot
Duality-based adaptivity in finite element discretization of heterogeneous multiscale problems
Editorial review for independent work. ICSAC — the Institute for Complexity Science and Advanced Computing — runs a structured editorial panel for researchers publishing outside journals, and publishes on CiteStamp rails. Submission is free and goes through ORCID: icsacinstitute.org/submit.