EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 48 2 (2014) 517-552 Article references

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:

Algebraic Construction of Adaptive Coarse Spaces for Two-Level Schwarz Preconditioners

Alexander Heinlein and Kathrin Smetana
SIAM Journal on Scientific Computing 47 (2) A1170 (2025)
https://doi.org/10.1137/23M1618193

Spectral ACMS: A Robust Localized Approximated Component Mode Synthesis Method

Alexandre L. Madureira and Marcus Sarkis
SIAM Journal on Numerical Analysis 63 (3) 1055 (2025)
https://doi.org/10.1137/24M1665362

Solving a class of multi-scale elliptic PDEs by Fourier-based mixed physics informed neural networks

Xi'an Li, Jinran Wu, Xin Tai, Jianhua Xu and You-Gan Wang
Journal of Computational Physics 508 113012 (2024)
https://doi.org/10.1016/j.jcp.2024.113012

Rough Polyharmonic Splines Method forOptimal Control Problem Governed by Elliptic Systems with Rough Coefficient

焦燕 曾
Pure Mathematics 14 (12) 56 (2024)
https://doi.org/10.12677/PM.2024.1412406

A reduced basis super-localized orthogonal decomposition for reaction-convection-diffusion problems

Francesca Bonizzoni, Moritz Hauck and Daniel Peterseim
Journal of Computational Physics 499 112698 (2024)
https://doi.org/10.1016/j.jcp.2023.112698

Computational Multiscale Methods for Nondivergence-Form Elliptic Partial Differential Equations

Philip Freese, Dietmar Gallistl, Daniel Peterseim and Timo Sprekeler
Computational Methods in Applied Mathematics 24 (3) 649 (2024)
https://doi.org/10.1515/cmam-2023-0040

A Multiscale Finite Element Method for an Elliptic Distributed Optimal Control Problem with Rough Coefficients and Control Constraints

Susanne C. Brenner, José C. Garay and Li-yeng Sung
Journal of Scientific Computing 100 (2) (2024)
https://doi.org/10.1007/s10915-024-02590-6

Exponentially Convergent Multiscale Finite Element Method

Yifan Chen, Thomas Y. Hou and Yixuan Wang
Communications on Applied Mathematics and Computation 6 (2) 862 (2024)
https://doi.org/10.1007/s42967-023-00260-2

Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations

Yifan Chen, Thomas Y. Hou and Yixuan Wang
Multiscale Modeling & Simulation 21 (3) 849 (2023)
https://doi.org/10.1137/22M1507802

Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations

Tina Mai, Siu Wun Cheung and Jun Sur Richard Park
Journal of Computational Physics 477 111915 (2023)
https://doi.org/10.1016/j.jcp.2023.111915

Localized Model Reduction for Nonlinear Elliptic Partial Differential Equations: Localized Training, Partition of Unity, and Adaptive Enrichment

Kathrin Smetana and Tommaso Taddei
SIAM Journal on Scientific Computing 45 (3) A1300 (2023)
https://doi.org/10.1137/22M148402X

Subspace decomposition based DNN algorithm for elliptic type multi-scale PDEs

Xi-An Li, Zhi-Qin John Xu and Lei Zhang
Journal of Computational Physics 488 112242 (2023)
https://doi.org/10.1016/j.jcp.2023.112242

An Elliptic Local Problem with Exponential Decay of the Resonance Error for Numerical Homogenization

Assyr Abdulle, Doghonay Arjmand and Edoardo Paganoni
Multiscale Modeling & Simulation 21 (2) 513 (2023)
https://doi.org/10.1137/21M1452123

Neural Network Approximation of Coarse-Scale Surrogates in Numerical Homogenization

Fabian Kröpfl, Roland Maier and Daniel Peterseim
Multiscale Modeling & Simulation 21 (4) 1457 (2023)
https://doi.org/10.1137/22M1524278

Randomized Quasi-Optimal Local Approximation Spaces in Time

Julia Schleuß, Kathrin Smetana and Lukas ter Maat
SIAM Journal on Scientific Computing 45 (3) A1066 (2023)
https://doi.org/10.1137/22M1481002

Online Adaptive Algorithm for Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method

Sai-Mang Pun and Siu Wun Cheung
Multiscale Modeling & Simulation 21 (1) 168 (2023)
https://doi.org/10.1137/21M1402625

An efficient algorithm for solving elliptic problems on percolation clusters

Chenlin Gu
The Annals of Applied Probability 32 (4) (2022)
https://doi.org/10.1214/21-AAP1748

A Space-Time Multiscale Method for Parabolic Problems

Per Ljung, Roland Maier and Axel Målqvist
Multiscale Modeling & Simulation 20 (2) 714 (2022)
https://doi.org/10.1137/21M1446605

Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data

Yifan Chen and Thomas Y. Hou
Multiscale Modeling & Simulation 20 (1) 188 (2022)
https://doi.org/10.1137/20M1372214

Optimal Local Approximation Spaces for Parabolic Problems

Julia Schleuß and Kathrin Smetana
Multiscale Modeling & Simulation 20 (1) 551 (2022)
https://doi.org/10.1137/20M1384294

Novel Design and Analysis of Generalized Finite Element Methods Based on Locally Optimal Spectral Approximations

Chupeng Ma, Robert Scheichl and Tim Dodwell
SIAM Journal on Numerical Analysis 60 (1) 244 (2022)
https://doi.org/10.1137/21M1406179

Iterative oversampling technique for constraint energy minimizing generalized multiscale finite element method in the mixed formulation

Siu Wun Cheung, Eric Chung, Yalchin Efendiev, Wing Tat Leung and Sai-Mang Pun
Applied Mathematics and Computation 415 126622 (2022)
https://doi.org/10.1016/j.amc.2021.126622

Super-localization of elliptic multiscale problems

Moritz Hauck and Daniel Peterseim
Mathematics of Computation 92 (341) 981 (2022)
https://doi.org/10.1090/mcom/3798

Subspace Decomposition Based Dnn Algorithm for Elliptic-Type Multi-Scale Pdes

Xi-An Li, Zhi-Qin John Xu and Lei Zhang
SSRN Electronic Journal (2022)
https://doi.org/10.2139/ssrn.4020731

Angles between subspaces and nearly optimal approximation in GFEM

Robert Lipton, Paul Sinz and Michael Stuebner
Computer Methods in Applied Mechanics and Engineering 402 115628 (2022)
https://doi.org/10.1016/j.cma.2022.115628

Numerical upscaling for heterogeneous materials in fractured domains

Fredrik Hellman, Axel Målqvist and Siyang Wang
ESAIM: Mathematical Modelling and Numerical Analysis 55 S761 (2021)
https://doi.org/10.1051/m2an/2020061

Explicit and Energy-Conserving Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method for Wave Propagation in Heterogeneous Media

Siu Wun Cheung, Eric T. Chung, Yalchin Efendiev and Wing Tat Leung
Multiscale Modeling & Simulation 19 (4) 1736 (2021)
https://doi.org/10.1137/20M1363832

A High-Order Approach to Elliptic Multiscale Problems with General Unstructured Coefficients

Roland Maier
SIAM Journal on Numerical Analysis 59 (2) 1067 (2021)
https://doi.org/10.1137/20M1364321

Iterated Numerical Homogenization for MultiScale Elliptic Equations with Monotone Nonlinearity

Xinliang Liu, Eric Chung and Lei Zhang
Multiscale Modeling & Simulation 19 (4) 1601 (2021)
https://doi.org/10.1137/21M1389900

Hybrid Localized Spectral Decomposition for Multiscale Problems

Alexandre L. Madureira and Marcus Sarkis
SIAM Journal on Numerical Analysis 59 (2) 829 (2021)
https://doi.org/10.1137/20M1314896

An iterative method for elliptic problems with rapidly oscillating coefficients

Scott Armstrong, Antti Hannukainen, Tuomo Kuusi and Jean-Christophe Mourrat
ESAIM: Mathematical Modelling and Numerical Analysis 55 (1) 37 (2021)
https://doi.org/10.1051/m2an/2020080

Compression, Inversion, and Approximate PCA of Dense Kernel Matrices at Near-Linear Computational Complexity

Florian Schäfer, T. J. Sullivan and Houman Owhadi
Multiscale Modeling & Simulation 19 (2) 688 (2021)
https://doi.org/10.1137/19M129526X

Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions

Yifan Chen, Thomas Y. Hou and Yixuan Wang
Multiscale Modeling & Simulation 19 (2) 980 (2021)
https://doi.org/10.1137/20M1352922

Reconstruction of Quasi-Local Numerical Effective Models from Low-Resolution Measurements

A. Caiazzo, R. Maier and D. Peterseim
Journal of Scientific Computing 85 (1) (2020)
https://doi.org/10.1007/s10915-020-01304-y

Multiscale-Spectral GFEM and optimal oversampling

Ivo Babuška, Robert Lipton, Paul Sinz and Michael Stuebner
Computer Methods in Applied Mechanics and Engineering 364 112960 (2020)
https://doi.org/10.1016/j.cma.2020.112960

Rough polyharmonic splines method for optimal control problem governed by parabolic systems with rough coefficient

Jiaoyan Zeng, Yanping Chen and Guichang Liu
Computers & Mathematics with Applications 80 (1) 121 (2020)
https://doi.org/10.1016/j.camwa.2020.03.001

Constraint energy minimizing generalized multiscale discontinuous Galerkin method

Siu Wun Cheung, Eric T. Chung and Wing Tat Leung
Journal of Computational and Applied Mathematics 380 112960 (2020)
https://doi.org/10.1016/j.cam.2020.112960

Randomized Sampling for Basis Function Construction in Generalized Finite Element Methods

Ke Chen, Qin Li, Jianfeng Lu and Stephen J. Wright
Multiscale Modeling & Simulation 18 (2) 1153 (2020)
https://doi.org/10.1137/18M1166432

Random Sampling and Efficient Algorithms for Multiscale PDEs

Ke Chen, Qin Li, Jianfeng Lu and Stephen J. Wright
SIAM Journal on Scientific Computing 42 (5) A2974 (2020)
https://doi.org/10.1137/18M1207430

Uniform estimate of an iterative method for elliptic problems with rapidly oscillating coefficients

Chenlin Gu
Stochastics and Partial Differential Equations: Analysis and Computations 8 (4) 787 (2020)
https://doi.org/10.1007/s40072-019-00159-1

Numerical Homogenization of Elliptic PDEs with Similar Coefficients

Fredrik Hellman and Axel Målqvist
Multiscale Modeling & Simulation 17 (2) 650 (2019)
https://doi.org/10.1137/18M1189701

Fast Eigenpairs Computation with Operator Adapted Wavelets and Hierarchical Subspace Correction

Hehu Xie, Lei Zhang and Houman Owhadi
SIAM Journal on Numerical Analysis 57 (6) 2519 (2019)
https://doi.org/10.1137/18M1194079

Operator-adapted wavelets for finite-element differential forms

Max Budninskiy, Houman Owhadi and Mathieu Desbrun
Journal of Computational Physics 388 144 (2019)
https://doi.org/10.1016/j.jcp.2019.02.018

Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization

Houman Owhadi and Clint Scovel
Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization (2019)
https://doi.org/10.1017/9781108594967

Online Adaptive Basis Enrichment for Mixed CEM-GMsFEM

Eric T. Chung and Sai-Mang Pun
Multiscale Modeling & Simulation 17 (4) 1103 (2019)
https://doi.org/10.1137/18M1222995

Efficient implementation of the localized orthogonal decomposition method

Christian Engwer, Patrick Henning, Axel Målqvist and Daniel Peterseim
Computer Methods in Applied Mechanics and Engineering 350 123 (2019)
https://doi.org/10.1016/j.cma.2019.02.040

A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach

Thomas Y. Hou, Dingjiong Ma and Zhiwen Zhang
Multiscale Modeling & Simulation 17 (2) 826 (2019)
https://doi.org/10.1137/18M1205844

Multiresolution operator decomposition for flow simulation in fractured porous media

Qingfu Zhang, Houman Owhadi, Jun Yao, Florian Schäfer, Zhaoqin Huang and Yang Li
Journal of Computational Physics 391 381 (2019)
https://doi.org/10.1016/j.jcp.2018.12.032

Constraint energy minimizing generalized multiscale finite element method in the mixed formulation

Eric Chung, Yalchin Efendiev and Wing Tat Leung
Computational Geosciences 22 (3) 677 (2018)
https://doi.org/10.1007/s10596-018-9719-7

Fast online generalized multiscale finite element method using constraint energy minimization

Eric T. Chung, Yalchin Efendiev and Wing Tat Leung
Journal of Computational Physics 355 450 (2018)
https://doi.org/10.1016/j.jcp.2017.11.022

Numerical coarsening using discontinuous shape functions

Jiong Chen, Hujun Bao, Tianyu Wang, Mathieu Desbrun and Jin Huang
ACM Transactions on Graphics 37 (4) 1 (2018)
https://doi.org/10.1145/3197517.3201386

Localized harmonic characteristic basis functions for multiscale finite element methods

Leonardo A. Poveda, Juan Galvis and Victor M. Calo
Computational and Applied Mathematics 37 (2) 1986 (2018)
https://doi.org/10.1007/s40314-017-0431-3

Constraint Energy Minimizing Generalized Multiscale Finite Element Method

Eric T. Chung, Yalchin Efendiev and Wing Tat Leung
Computer Methods in Applied Mechanics and Engineering 339 298 (2018)
https://doi.org/10.1016/j.cma.2018.04.010

An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients

Thomas Y. Hou, Feng-Nan Hwang, Pengfei Liu and Chien-Chou Yao
Journal of Computational Physics 336 375 (2017)
https://doi.org/10.1016/j.jcp.2017.02.002

Sparse operator compression of higher-order elliptic operators with rough coefficients

Thomas Y. Hou and Pengchuan Zhang
Research in the Mathematical Sciences 4 (1) (2017)
https://doi.org/10.1186/s40687-017-0113-1

Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients

Houman Owhadi and Lei Zhang
Journal of Computational Physics 347 99 (2017)
https://doi.org/10.1016/j.jcp.2017.06.037

Computation of Quasi-Local Effective Diffusion Tensors and Connections to the Mathematical Theory of Homogenization

D. Gallistl and D. Peterseim
Multiscale Modeling & Simulation 15 (4) 1530 (2017)
https://doi.org/10.1137/16M1088533

Contrast Independent Localization of Multiscale Problems

Fredrik Hellman and Axel Målqvist
Multiscale Modeling & Simulation 15 (4) 1325 (2017)
https://doi.org/10.1137/16M1100460

Estimates for the Upscaling Error in Heterogeneous Multiscale Methods for Wave Propagation Problems in Locally Periodic Media

Doghonay Arjmand and Olof Runborg
Multiscale Modeling & Simulation 15 (2) 948 (2017)
https://doi.org/10.1137/16M1074436

Multigrid with Rough Coefficients and Multiresolution Operator Decomposition from Hierarchical Information Games

Houman Owhadi
SIAM Review 59 (1) 99 (2017)
https://doi.org/10.1137/15M1013894

Exploring the Locally Low Dimensional Structure in Solving Random Elliptic PDEs

Thomas Y. Hou, Qin Li and Pengchuan Zhang
Multiscale Modeling & Simulation 15 (2) 661 (2017)
https://doi.org/10.1137/16M1077611

Multiscale methods for problems with complex geometry

Daniel Elfverson, Mats G. Larson and Axel Målqvist
Computer Methods in Applied Mechanics and Engineering 321 103 (2017)
https://doi.org/10.1016/j.cma.2017.03.023

A Sparse Decomposition of Low Rank Symmetric Positive Semidefinite Matrices

Thomas Y. Hou, Qin Li and Pengchuan Zhang
Multiscale Modeling & Simulation 15 (1) 410 (2017)
https://doi.org/10.1137/16M107760X

A multiscale model reduction method for nonlinear monotone elliptic equations in heterogeneous media

Shuai Ye, Ke Shi, Yalchin Efendiev and Eric Chung
Networks and Heterogeneous Media 12 (4) 619 (2017)
https://doi.org/10.3934/nhm.2017025

An Asymptotic Preserving Method for Transport Equations with Oscillatory Scattering Coefficients

Qin Li and Jianfeng Lu
Multiscale Modeling & Simulation 15 (4) 1694 (2017)
https://doi.org/10.1137/16M109212X

Robust Numerical Upscaling of Elliptic Multiscale Problems at High Contrast

Daniel Peterseim and Robert Scheichl
Computational Methods in Applied Mathematics 16 (4) 579 (2016)
https://doi.org/10.1515/cmam-2016-0022

High-resolution interaction with corotational coarsening models

Rosell Torres, Alejandro Rodríguez, José M. Espadero and Miguel A. Otaduy
ACM Transactions on Graphics 35 (6) 1 (2016)
https://doi.org/10.1145/2980179.2982414

Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Daniel Peterseim
Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 343 (2016)
https://doi.org/10.1007/978-3-319-41640-3_11

Reduction in the Resonance Error in Numerical Homogenization II: Correctors and Extrapolation

Antoine Gloria and Zakaria Habibi
Foundations of Computational Mathematics 16 (1) 217 (2016)
https://doi.org/10.1007/s10208-015-9246-z

A multiscale method for linear elasticity reducing Poisson locking

Patrick Henning and Anna Persson
Computer Methods in Applied Mechanics and Engineering 310 156 (2016)
https://doi.org/10.1016/j.cma.2016.06.034

Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients

Pengfei Liu and Thomas Y. Hou
Discrete and Continuous Dynamical Systems 36 (8) 4451 (2016)
https://doi.org/10.3934/dcds.2016.36.4451

Two-level additive Schwarz methods using rough polyharmonic splines-based coarse spaces

Rui Du and Lei Zhang
Chinese Annals of Mathematics, Series B 36 (5) 803 (2015)
https://doi.org/10.1007/s11401-015-0977-6

Adaptive heterogeneous multiscale methods for immiscible two-phase flow in porous media

Patrick Henning, Mario Ohlberger and Ben Schweizer
Computational Geosciences 19 (1) 99 (2015)
https://doi.org/10.1007/s10596-014-9455-6

Localized Orthogonal Decomposition Techniques for Boundary Value Problems

Patrick Henning and Axel Målqvist
SIAM Journal on Scientific Computing 36 (4) A1609 (2014)
https://doi.org/10.1137/130933198