EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 47 1 (2013) 253-280 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:

This article has been cited by the following article(s):

Sparse Polynomial Approximations for Affine Parametric Saddle Point Problems

Peng Chen and Omar Ghattas
Vietnam Journal of Mathematics 51 (1) 151 (2023)
DOI: 10.1007/s10013-022-00584-1
See this article

Коллокационная аппроксимация глубокими $\mathrm{ReLU}$-нейронными сетями решений параметрических и стохастических уравнений с частными производными c логнормальными входами

Dung Dinh and Зунг Динь
Математический сборник 214 (4) 38 (2023)
DOI: 10.4213/sm9791
See this article

High-Dimensional Optimization and Probability

Ben Adcock, Juan M. Cardenas, Nick Dexter and Sebastian Moraga
Springer Optimization and Its Applications, High-Dimensional Optimization and Probability 191 9 (2022)
DOI: 10.1007/978-3-031-00832-0_2
See this article

Trace Class in Separable Reflexive Banach Spaces, Lidskii Theorem

Mykola Yaremenko
EQUATIONS 2 123 (2022)
DOI: 10.37394/232021.2022.2.19
See this article

The Random Feature Model for Input-Output Maps between Banach Spaces

Nicholas H. Nelsen and Andrew M. Stuart
SIAM Journal on Scientific Computing 43 (5) A3212 (2021)
DOI: 10.1137/20M133957X
See this article

Model Reduction And Neural Networks For Parametric PDEs

Kaushik Bhattacharya, Bamdad Hosseini, Nikola B. Kovachki and Andrew M. Stuart
The SMAI journal of computational mathematics 7 121 (2021)
DOI: 10.5802/smai-jcm.74
See this article

Shape Holomorphy of the Calderón Projector for the Laplacian in $${\mathbb {R}}^2$$

Fernando Henríquez and Christoph Schwab
Integral Equations and Operator Theory 93 (4) (2021)
DOI: 10.1007/s00020-021-02653-5
See this article

Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs

Dinh Dũng
ESAIM: Mathematical Modelling and Numerical Analysis 55 (3) 1163 (2021)
DOI: 10.1051/m2an/2021017
See this article

Nonlinear methods for model reduction

Andrea Bonito, Albert Cohen, Ronald DeVore, et al.
ESAIM: Mathematical Modelling and Numerical Analysis 55 (2) 507 (2021)
DOI: 10.1051/m2an/2020057
See this article

Polynomial Approximation of Anisotropic Analytic Functions of Several Variables

Andrea Bonito, Ronald DeVore, Diane Guignard, Peter Jantsch and Guergana Petrova
Constructive Approximation 53 (2) 319 (2021)
DOI: 10.1007/s00365-020-09511-4
See this article

Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Francesca Bonizzoni and Fabio Nobile
Computers & Mathematics with Applications 80 (12) 2925 (2020)
DOI: 10.1016/j.camwa.2020.10.014
See this article

A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data

J. Lang, R. Scheichl and D. Silvester
Journal of Computational Physics 419 109692 (2020)
DOI: 10.1016/j.jcp.2020.109692
See this article

Convergence rates of high dimensional Smolyak quadrature

Jakob Zech and Christoph Schwab
ESAIM: Mathematical Modelling and Numerical Analysis 54 (4) 1259 (2020)
DOI: 10.1051/m2an/2020003
See this article

Multilevel approximation of parametric and stochastic PDES

Jakob Zech, Dinh Dũng and Christoph Schwab
Mathematical Models and Methods in Applied Sciences 29 (09) 1753 (2019)
DOI: 10.1142/S0218202519500349
See this article

Linear collective collocation approximation for parametric and stochastic elliptic PDEs

Dinh Dũng
Sbornik: Mathematics 210 (4) 565 (2019)
DOI: 10.1070/SM9068
See this article

IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains

Joakim Beck, Lorenzo Tamellini and Raúl Tempone
Computer Methods in Applied Mechanics and Engineering 351 330 (2019)
DOI: 10.1016/j.cma.2019.03.042
See this article

A mixed ℓ1 regularization approach for sparse simultaneous approximation of parameterized PDEs

Nick Dexter, Hoang Tran and Clayton Webster
ESAIM: Mathematical Modelling and Numerical Analysis 53 (6) 2025 (2019)
DOI: 10.1051/m2an/2019048
See this article

Линейная совместная коллокационная аппроксимация для параметрических и стохастических эллиптических дифференциальных уравнений с частными производными

Dung Dinh and Зунг Динь
Математический сборник 210 (4) 103 (2019)
DOI: 10.4213/sm9068
See this article

Shape Holomorphy of the Stationary Navier--Stokes Equations

Albert Cohen, Christoph Schwab and Jakob Zech
SIAM Journal on Mathematical Analysis 50 (2) 1720 (2018)
DOI: 10.1137/16M1099406
See this article

A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities

Anthony Nouy and Florent Pled
ESAIM: Mathematical Modelling and Numerical Analysis 52 (5) 1763 (2018)
DOI: 10.1051/m2an/2018025
See this article

Quasi--Monte Carlo Integration for Affine-Parametric, Elliptic PDEs: Local Supports and Product Weights

Robert N. Gantner, Lukas Herrmann and Christoph Schwab
SIAM Journal on Numerical Analysis 56 (1) 111 (2018)
DOI: 10.1137/16M1082597
See this article

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

Diane Guignard and Fabio Nobile
SIAM Journal on Numerical Analysis 56 (5) 3121 (2018)
DOI: 10.1137/17M1155454
See this article

Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients

Hoang Tran, Clayton G. Webster and Guannan Zhang
Numerische Mathematik 137 (2) 451 (2017)
DOI: 10.1007/s00211-017-0878-6
See this article

Handbook of Uncertainty Quantification

Max Gunzburger, Clayton G. Webster and Guannan Zhang
Handbook of Uncertainty Quantification 717 (2017)
DOI: 10.1007/978-3-319-12385-1_29
See this article

Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients

Markus Bachmayr, Albert Cohen and Giovanni Migliorati
ESAIM: Mathematical Modelling and Numerical Analysis 51 (1) 321 (2017)
DOI: 10.1051/m2an/2016045
See this article

Compressed Sensing and its Applications

Ben Adcock, Simone Brugiapaglia and Clayton G. Webster
Applied and Numerical Harmonic Analysis, Compressed Sensing and its Applications 93 (2017)
DOI: 10.1007/978-3-319-69802-1_3
See this article

Electromagnetic wave scattering by random surfaces: Shape holomorphy

Carlos Jerez-Hanckes, Christoph Schwab and Jakob Zech
Mathematical Models and Methods in Applied Sciences 27 (12) 2229 (2017)
DOI: 10.1142/S0218202517500439
See this article

Data Assimilation in Reduced Modeling

Peter Binev, Albert Cohen, Wolfgang Dahmen, et al.
SIAM/ASA Journal on Uncertainty Quantification 5 (1) 1 (2017)
DOI: 10.1137/15M1025384
See this article

Handbook of Uncertainty Quantification

Peng Chen and Christoph Schwab
Handbook of Uncertainty Quantification 937 (2017)
DOI: 10.1007/978-3-319-12385-1_70
See this article

Numerical study of a parametric parabolic equation and a related inverse boundary value problem

Lauri Mustonen
Inverse Problems 32 (10) 105008 (2016)
DOI: 10.1088/0266-5611/32/10/105008
See this article

Hyperbolic cross approximation in infinite dimensions

Dinh Dũng and Michael Griebel
Journal of Complexity 33 55 (2016)
DOI: 10.1016/j.jco.2015.09.006
See this article

Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs

F. Nobile, L. Tamellini and R. Tempone
Numerische Mathematik 134 (2) 343 (2016)
DOI: 10.1007/s00211-015-0773-y
See this article

A dynamically adaptive sparse grids method for quasi-optimal interpolation of multidimensional functions

Miroslav K. Stoyanov and Clayton G. Webster
Computers & Mathematics with Applications 71 (11) 2449 (2016)
DOI: 10.1016/j.camwa.2015.12.045
See this article

Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

F. Bonizzoni, F. Nobile and D. Kressner
Computer Methods in Applied Mechanics and Engineering 308 349 (2016)
DOI: 10.1016/j.cma.2016.05.026
See this article

Sparse Grids and Applications - Stuttgart 2014

Peng Chen and Christoph Schwab
Lecture Notes in Computational Science and Engineering, Sparse Grids and Applications - Stuttgart 2014 109 1 (2016)
DOI: 10.1007/978-3-319-28262-6_1
See this article

Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems

Angela Kunoth and Christoph Schwab
SIAM/ASA Journal on Uncertainty Quantification 4 (1) 1034 (2016)
DOI: 10.1137/15M1041390
See this article

Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

Peng Chen and Christoph Schwab
Journal of Computational Physics 316 470 (2016)
DOI: 10.1016/j.jcp.2016.02.055
See this article

Handbook of Uncertainty Quantification

Peng Chen and Christoph Schwab
Handbook of Uncertainty Quantification 1 (2015)
DOI: 10.1007/978-3-319-11259-6_70-1
See this article

Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs

Abdellah Chkifa, Albert Cohen and Christoph Schwab
Journal de Mathématiques Pures et Appliquées 103 (2) 400 (2015)
DOI: 10.1016/j.matpur.2014.04.009
See this article

Sampling Theory, a Renaissance

Albert Cohen and Abdellah Chkifa
Applied and Numerical Harmonic Analysis, Sampling Theory, a Renaissance 437 (2015)
DOI: 10.1007/978-3-319-19749-4_12
See this article

Approximate methods for stochastic eigenvalue problems

H. Hakula, V. Kaarnioja and M. Laaksonen
Applied Mathematics and Computation 267 664 (2015)
DOI: 10.1016/j.amc.2014.12.112
See this article

Hybrid Stochastic Finite Element Method for Mechanical Vibration Problems

Harri Hakula and Mikael Laaksonen
Shock and Vibration 2015 1 (2015)
DOI: 10.1155/2015/812069
See this article

A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes

Martin Eigel, Claude Jeffrey Gittelson, Christoph Schwab and Elmar Zander
ESAIM: Mathematical Modelling and Numerical Analysis 49 (5) 1367 (2015)
DOI: 10.1051/m2an/2015017
See this article

Approximation of high-dimensional parametric PDEs

Albert Cohen and Ronald DeVore
Acta Numerica 24 1 (2015)
DOI: 10.1017/S0962492915000033
See this article

Encyclopedia of Applied and Computational Mathematics

Christoph Schwab
Encyclopedia of Applied and Computational Mathematics 903 (2015)
DOI: 10.1007/978-3-540-70529-1_526
See this article

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Abdellah Chkifa, Albert Cohen, Giovanni Migliorati, Fabio Nobile and Raul Tempone
ESAIM: Mathematical Modelling and Numerical Analysis 49 (3) 815 (2015)
DOI: 10.1051/m2an/2014050
See this article

Handbook of Uncertainty Quantification

Max Gunzburger, Clayton G. Webster and Guannan Zhang
Handbook of Uncertainty Quantification 1 (2015)
DOI: 10.1007/978-3-319-11259-6_29-1
See this article

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Joakim Beck, Fabio Nobile, Lorenzo Tamellini and Raúl Tempone
Computers & Mathematics with Applications 67 (4) 732 (2014)
DOI: 10.1016/j.camwa.2013.03.004
See this article

Modeling, Simulation and Optimization of Complex Processes - HPSC 2012

Markus Hansen, Claudia Schillings and Christoph Schwab
Modeling, Simulation and Optimization of Complex Processes - HPSC 2012 63 (2014)
DOI: 10.1007/978-3-319-09063-4_6
See this article

Perturbation Analysis for the Darcy Problem with Log-Normal Permeability

Francesca Bonizzoni and Fabio Nobile
SIAM/ASA Journal on Uncertainty Quantification 2 (1) 223 (2014)
DOI: 10.1137/130949415
See this article

Greedy Algorithms for High-Dimensional Eigenvalue Problems

Eric Cancès, Virginie Ehrlacher and Tony Lelièvre
Constructive Approximation 40 (3) 387 (2014)
DOI: 10.1007/s00365-014-9266-y
See this article

High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs

Abdellah Chkifa, Albert Cohen and Christoph Schwab
Foundations of Computational Mathematics 14 (4) 601 (2014)
DOI: 10.1007/s10208-013-9154-z
See this article

Extraction of Quantifiable Information from Complex Systems

Wolfgang Dahmen, Chunyan Huang, Gitta Kutyniok, et al.
Lecture Notes in Computational Science and Engineering, Extraction of Quantifiable Information from Complex Systems 102 25 (2014)
DOI: 10.1007/978-3-319-08159-5_2
See this article

Sparsity in Bayesian inversion of parametric operator equations

Cl Schillings and Ch Schwab
Inverse Problems 30 (6) 065007 (2014)
DOI: 10.1088/0266-5611/30/6/065007
See this article

Inverse modeling of geochemical and mechanical compaction in sedimentary basins through Polynomial Chaos Expansion

G. Porta, L. Tamellini, V. Lever and M. Riva
Water Resources Research 50 (12) 9414 (2014)
DOI: 10.1002/2014WR015838
See this article

On the Lebesgue constant of Leja sequences for the complex unit disk and of their real projection

Moulay Abdellah Chkifa
Journal of Approximation Theory 166 176 (2013)
DOI: 10.1016/j.jat.2012.11.005
See this article

Sparse, adaptive Smolyak quadratures for Bayesian inverse problems

Claudia Schillings and Christoph Schwab
Inverse Problems 29 (6) 065011 (2013)
DOI: 10.1088/0266-5611/29/6/065011
See this article

Complexity analysis of accelerated MCMC methods for Bayesian inversion

Viet Ha Hoang, Christoph Schwab and Andrew M Stuart
Inverse Problems 29 (8) 085010 (2013)
DOI: 10.1088/0266-5611/29/8/085010
See this article

Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs

Angela Kunoth and Christoph Schwab
SIAM Journal on Control and Optimization 51 (3) 2442 (2013)
DOI: 10.1137/110847597
See this article

A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty

D. P. Kouri, M. Heinkenschloss, D. Ridzal and B. G. van Bloemen Waanders
SIAM Journal on Scientific Computing 35 (4) A1847 (2013)
DOI: 10.1137/120892362
See this article

Uniformly convergent adaptive methods for a class of parametric operator equations

Claude Jeffrey Gittelson
ESAIM: Mathematical Modelling and Numerical Analysis 46 (6) 1485 (2012)
DOI: 10.1051/m2an/2012013
See this article