Error estimates for some quasi-interpolation operators
ESAIM: M2AN, 33 4 (1999) 695-713
Published online: 2002-08-15
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
A quasi-interpolation operator yielding fully computable error bounds
Theophile Chaumont-Frelet and Martin VohralíkESAIM: Mathematical Modelling and Numerical Analysis 60 (1) 1 (2026)
https://doi.org/10.1051/m2an/2025091
Finite-time gradient blow-up and shock formation in Israel-Stewart theory: Bulk, shear, and diffusion regimes
Fábio S. BemficaPhysical Review E 112 (6) (2025)
https://doi.org/10.1103/blhw-xplr
Deep Ritz - Finite element methods: Neural network methods trained with finite elements
Georgios Grekas and Charalambos G. MakridakisComputer Methods in Applied Mechanics and Engineering 437 117798 (2025)
https://doi.org/10.1016/j.cma.2025.117798
60 235 (2025)
https://doi.org/10.1016/bs.aams.2025.02.006
9 (2024)
https://doi.org/10.1007/978-981-97-3577-8_2
https://doi.org/10.1016/bs.aams.2024.03.002
Numerical comparison of three a posteriori error estimators for nonconforming finite element method
B. Achchab, A. Agouzal, K. Bouihat and A. MajdoubiMoroccan Journal of Pure and Applied Analysis 9 (1) 1 (2023)
https://doi.org/10.2478/mjpaa-2023-0001
Efficient a Posteriori Error Control of a Concurrent Multiscale Method with Sharp Interface for Crystalline Defects
Yangshuai Wang and Hao WangJournal of Scientific Computing 97 (2) (2023)
https://doi.org/10.1007/s10915-023-02362-8
A Posteriori Error Estimates for Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
Andrea Cangiani, Zhaonan Dong and Emmanuil H. GeorgoulisSIAM Journal on Numerical Analysis 61 (5) 2352 (2023)
https://doi.org/10.1137/22M1516701
Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem
Zhaonan Dong and Alexandre ErnSIAM Journal on Numerical Analysis 60 (5) 2626 (2022)
https://doi.org/10.1137/21M1408555
Numerical homogenization of fractal interface problems
Ralf Kornhuber, Joscha Podlesny and Harry YserentantESAIM: Mathematical Modelling and Numerical Analysis 56 (4) 1451 (2022)
https://doi.org/10.1051/m2an/2022046
A simple virtual element-based flux recovery on quadtree
Shuhao CaoElectronic Research Archive 29 (6) 3629 (2021)
https://doi.org/10.3934/era.2021054
A posteriori error estimates and an adaptive finite element solution for the system of unsteady convection-diffusion-reaction equations in fluidized beds
V. Dhanya Varma, Suresh Kumar Nadupuri and Nagaiah ChamakuriApplied Numerical Mathematics 163 108 (2021)
https://doi.org/10.1016/j.apnum.2021.01.012
Sparse Grids and Applications - Munich 2018
Fabio Nobile and Eva VidličkováLecture Notes in Computational Science and Engineering, Sparse Grids and Applications - Munich 2018 144 127 (2021)
https://doi.org/10.1007/978-3-030-81362-8_6
A dimension-reduction model for brittle fractures on thin shells with mesh adaptivity
Stefano Almi, Sandro Belz, Stefano Micheletti and Simona PerottoMathematical Models and Methods in Applied Sciences 31 (01) 37 (2021)
https://doi.org/10.1142/S0218202521500020
A posteriori error estimates for a fully discrete approximation of Sobolev equations
Serge Nicaise and Fatiha BekkoucheConfluentes Mathematici 11 (1) 3 (2019)
https://doi.org/10.5802/cml.53
Anisotropic interpolation error estimate for arbitrary quadrilateral isoparametric elements
Gabriel MonzónNumerische Mathematik 143 (2) 315 (2019)
https://doi.org/10.1007/s00211-019-01061-7
A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions
Hao Wang, Mingjie Liao, Ping Lin and Lei ZhangSIAM Journal on Scientific Computing 40 (4) A2087 (2018)
https://doi.org/10.1137/17M1131106
Residual error estimation for anisotropic Kirchhoff plates
Michael WeiseApplied Numerical Mathematics 125 10 (2018)
https://doi.org/10.1016/j.apnum.2017.10.007
Detection of thermal bridges from thermographic images by means of image processing approximation algorithms
Francesco Asdrubali, Giorgio Baldinelli, Francesco Bianchi, et al.Applied Mathematics and Computation 317 160 (2018)
https://doi.org/10.1016/j.amc.2017.08.058
1 (2017)
https://doi.org/10.1002/9781119176817.ecm2002m
A posteriori error estimates for the virtual element method
Andrea Cangiani, Emmanuil H. Georgoulis, Tristan Pryer and Oliver J. SuttonNumerische Mathematik 137 (4) 857 (2017)
https://doi.org/10.1007/s00211-017-0891-9
Convergence study of the h-adaptive PUM and the hp-adaptive FEM applied to eigenvalue problems in quantum mechanics
Denis Davydov, Tymofiy Gerasimov, Jean-Paul Pelteret and Paul SteinmannAdvanced Modeling and Simulation in Engineering Sciences 4 (1) (2017)
https://doi.org/10.1186/s40323-017-0093-0
The minimal angle condition for quadrilateral finite elements of arbitrary degree
Gabriel Acosta and Gabriel MonzónJournal of Computational and Applied Mathematics 317 218 (2017)
https://doi.org/10.1016/j.cam.2016.11.041
Analysis of blended atomistic/continuum hybrid methods
Xingjie Helen Li, Christoph Ortner, Alexander V. Shapeev and Brian Van KotenNumerische Mathematik 134 (2) 275 (2016)
https://doi.org/10.1007/s00211-015-0772-z
On optimal simplicial 3D meshes for minimizing the Hessian-based errors
Y. Mesri, M. Khalloufi and E. HachemApplied Numerical Mathematics 109 235 (2016)
https://doi.org/10.1016/j.apnum.2016.07.007
Pointwise and uniform approximation by multivariate neural network operators of the max-product type
Danilo Costarelli and Gianluca VintiNeural Networks 81 81 (2016)
https://doi.org/10.1016/j.neunet.2016.06.002
A discrete duality finite volume discretization of the vorticity‐velocity‐pressure stokes problem on almost arbitrary two‐dimensional grids
Sarah Delcourte and Pascal OmnesNumerical Methods for Partial Differential Equations 31 (1) 1 (2015)
https://doi.org/10.1002/num.21890
Constant-free explicit error estimator with sharp upper error bound property for adaptive FE analysis in elasticity and fracture
T. Gerasimov, E. Stein and P. WriggersInternational Journal for Numerical Methods in Engineering 101 (2) 79 (2015)
https://doi.org/10.1002/nme.4768
Ana posteriorierror estimation for the discrete duality finite volume discretization of the Stokes equations
Anh Ha Le and Pascal OmnesESAIM: Mathematical Modelling and Numerical Analysis 49 (3) 663 (2015)
https://doi.org/10.1051/m2an/2014057
Local high-order regularization and applications to hp-methods
M. Karkulik and J.M. MelenkComputers & Mathematics with Applications 70 (7) 1606 (2015)
https://doi.org/10.1016/j.camwa.2015.06.026
Application of hp-Adaptive Finite Element Method to Two-Scale Computation
Marta Oleksy and Witold CecotArchives of Computational Methods in Engineering 22 (1) 105 (2015)
https://doi.org/10.1007/s11831-014-9109-9
A recovery-based a posteriori error estimator for (curl) interface problems
Zhiqiang Cai and Shuhao CaoComputer Methods in Applied Mechanics and Engineering 296 169 (2015)
https://doi.org/10.1016/j.cma.2015.08.002
Estimation of computational homogenization error by explicit residual method
M. Oleksy and W. CecotComputers & Mathematics with Applications 66 (12) 2504 (2014)
https://doi.org/10.1016/j.camwa.2013.09.019
Shape-explicit constants for some boundary integral operators
Clemens PechsteinApplicable Analysis 92 (5) 949 (2013)
https://doi.org/10.1080/00036811.2011.643781
Verified Eigenvalue Evaluation for the Laplacian over Polygonal Domains of Arbitrary Shape
Xuefeng Liu and Shin'ichi OishiSIAM Journal on Numerical Analysis 51 (3) 1634 (2013)
https://doi.org/10.1137/120878446
A posteriorierror estimates forH1-Galerkin mixed finite-element method for parabolic problems
Madhusmita Tripathy and Rajen Kumar SinhaApplicable Analysis 92 (4) 855 (2013)
https://doi.org/10.1080/00036811.2011.643783
A posteriori error analysis of time-dependent Stokes problem by Chorin-Temam scheme
N. Kharrat and Z. MghazliCalcolo 49 (1) 41 (2012)
https://doi.org/10.1007/s10092-011-0044-y
On the Convergence of Adaptive Nonconforming Finite Element Methods for a Class of Convex Variational Problems
Christoph Ortner and Dirk PraetoriusSIAM Journal on Numerical Analysis 49 (1) 346 (2011)
https://doi.org/10.1137/090781073
An efficient, reliable and robust error estimator for elliptic problems in R3
Michael Holst, Jeffrey S. Ovall and Ryan SzypowskiApplied Numerical Mathematics 61 (5) 675 (2011)
https://doi.org/10.1016/j.apnum.2011.01.002
A Residual-Based A Posteriori Error Estimator for the Stokes�Darcy Coupled Problem
Ivo Babu�ka and Gabriel N. GaticaSIAM Journal on Numerical Analysis 48 (2) 498 (2010)
https://doi.org/10.1137/080727646
An Adaptive Finite Element Approximation of a Variational Model of Brittle Fracture
Siobhan Burke, Christoph Ortner and Endre S�liSIAM Journal on Numerical Analysis 48 (3) 980 (2010)
https://doi.org/10.1137/080741033
A convergent finite element-finite volume scheme for the compressible Stokes problem. Part I: The isothermal case
T. Gallouët, R. Herbin and J.-C. LatchéMathematics of Computation 78 (267) 1333 (2009)
https://doi.org/10.1090/S0025-5718-09-02216-9
Convergence analysis of a locally stabilized collocated finite volume scheme for incompressible flows
Robert Eymard, Raphaèle Herbin, Jean-Claude Latché and Bruno PiarESAIM: Mathematical Modelling and Numerical Analysis 43 (5) 889 (2009)
https://doi.org/10.1051/m2an/2009031
On the Interpolation Error Estimates for $Q_1$ Quadrilateral Finite Elements
Shipeng Mao, Serge Nicaise and Zhong-Ci ShiSIAM Journal on Numerical Analysis 47 (1) 467 (2009)
https://doi.org/10.1137/070700486
A Posteriori Error Estimation for the Discrete Duality Finite Volume Discretization of the Laplace Equation
Pascal Omnes, Yohan Penel and Yann RosenbaumSIAM Journal on Numerical Analysis 47 (4) 2782 (2009)
https://doi.org/10.1137/080735047
A Posteriori Existence in Numerical Computations
C. OrtnerSIAM Journal on Numerical Analysis 47 (4) 2550 (2009)
https://doi.org/10.1137/060668183
The Composite Mini Element�Coarse Mesh Computation of Stokes Flows on Complicated Domains
Daniel Peterseim and Stefan A. SauterSIAM Journal on Numerical Analysis 46 (6) 3181 (2008)
https://doi.org/10.1137/070704356
Convergence analysis of the Q1‐finite element method for elliptic problems with non‐boundary‐fitted meshes
Isabelle RamièreInternational Journal for Numerical Methods in Engineering 75 (9) 1007 (2008)
https://doi.org/10.1002/nme.2278
On estimators for eigenvalue/eigenvector approximations
Luka Grubišić and Jeffrey OvallMathematics of Computation 78 (266) 739 (2008)
https://doi.org/10.1090/S0025-5718-08-02181-9
A posteriori error estimates for a nonconforming finite element discretization of the time-dependent Stokes problem
S. Nicaise and N. SoualemJournal of Numerical Mathematics 15 (2) (2007)
https://doi.org/10.1515/JNUM.2007.007
A posteriori error estimates for a nonconforming finite element discretization of the time-dependent Stokes problem, II: Analysis of the spatial estimator
S. Nicaise and N. SoualemJournal of Numerical Mathematics 15 (3) (2007)
https://doi.org/10.1515/jnma.2007.010
Modified Taylor reproducing formulas and h-p clouds
Carlos ZuppaMathematics of Computation 77 (261) 243 (2007)
https://doi.org/10.1090/S0025-5718-07-02041-8
H 1-interpolation on quadrilateral and hexahedral meshes with hanging nodes
V. Heuveline and F. SchieweckComputing 80 (3) 203 (2007)
https://doi.org/10.1007/s00607-007-0233-3
On a stabilized colocated Finite Volume scheme for the Stokes problem
Robert Eymard, Raphaèle Herbin and Jean Claude LatchéESAIM: Mathematical Modelling and Numerical Analysis 40 (3) 501 (2006)
https://doi.org/10.1051/m2an:2006024
Interpolation error estimates in W 1,p for degenerate Q 1 isoparametric elements
Gabriel Acosta and Gabriel MonzónNumerische Mathematik 104 (2) 129 (2006)
https://doi.org/10.1007/s00211-006-0018-1
A posteriorierror estimates for a nonconforming finite element discretization of the heat equation
Serge Nicaise and Nadir SoualemESAIM: Mathematical Modelling and Numerical Analysis 39 (2) 319 (2005)
https://doi.org/10.1051/m2an:2005009
A posteriorierror analysis of the fully discretized time-dependent Stokes equations
Christine Bernardi and Rüdiger VerfürthESAIM: Mathematical Modelling and Numerical Analysis 38 (3) 437 (2004)
https://doi.org/10.1051/m2an:2004021
(2004)
https://doi.org/10.1002/0470091355.ecm002m
A posteriori analysis of the finite element discretization of some parabolic equations
A. Bergam, C. Bernardi and Z. MghazliMathematics of Computation 74 (251) 1117 (2004)
https://doi.org/10.1090/S0025-5718-04-01697-7
A posterioriError Estimates For the3D Stabilized Mortar Finite Element Method applied to the Laplace Equation
Zakaria BelhachmiESAIM: Mathematical Modelling and Numerical Analysis 37 (6) 991 (2003)
https://doi.org/10.1051/m2an:2003064
Geometric Analysis and Nonlinear Partial Differential Equations
W. Dörfler and K. G. SiebertGeometric Analysis and Nonlinear Partial Differential Equations 147 (2003)
https://doi.org/10.1007/978-3-642-55627-2_10
A POSTERIORI ANALYSIS OF A PENALTY METHOD AND APPLICATION TO THE STOKES PROBLEM
C. BERNARDI, V. GIRAULT and F. HECHTMathematical Models and Methods in Applied Sciences 13 (11) 1599 (2003)
https://doi.org/10.1142/S0218202503003057
Hermite interpolation of nonsmooth functions preserving boundary conditions
V. Girault and L. ScottMathematics of Computation 71 (239) 1043 (2002)
https://doi.org/10.1090/S0025-5718-02-01446-1
Error indicators for the mortar finite element discretization of the Laplace equation
Christine Bernardi and Frédéric HechtMathematics of Computation 71 (240) 1371 (2001)
https://doi.org/10.1090/S0025-5718-01-01401-6
Adaptive Lagrange–Galerkin methods for unsteady convection-diffusion problems
Paul Houston and Endre SüliMathematics of Computation 70 (233) 77 (2000)
https://doi.org/10.1090/S0025-5718-00-01187-X
Global and Local Error Analysis for the Residual-Free Bubbles Method Applied to Advection-Dominated Problems
Giancarlo SangalliSIAM Journal on Numerical Analysis 38 (5) 1496 (2000)
https://doi.org/10.1137/S0036142999365382
https://doi.org/10.1002/9781118032824.refs
Error Estimates for $\Cq_1$ Isoparametric Elements Satisfying a Weak Angle Condition
Gabriel Acosta and Ricardo G. DuránSIAM Journal on Numerical Analysis 38 (4) 1073 (2000)
https://doi.org/10.1137/S0036142999359104