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):

Recent Advances in Computational Engineering

Christopher Müller, Sebastian Ullmann and Jens Lang
Lecture Notes in Computational Science and Engineering, Recent Advances in Computational Engineering 124 63 (2018)
DOI: 10.1007/978-3-319-93891-2_5
See this article

Non-uniform Recovery Guarantees for Binary Measurements and Infinite-Dimensional Compressed Sensing

L. Thesing and A. C. Hansen
Journal of Fourier Analysis and Applications 27 (2) (2021)
DOI: 10.1007/s00041-021-09813-6
See this article

Near-optimal approximation methods for elliptic PDEs with lognormal coefficients

Albert Cohen and Giovanni Migliorati
Mathematics of Computation (2023)
DOI: 10.1090/mcom/3825
See this article

A sparse FFT approach for ODE with random coefficients

Maximilian Bochmann, Lutz Kämmerer and Daniel Potts
Advances in Computational Mathematics 46 (5) (2020)
DOI: 10.1007/s10444-020-09807-w
See this article

Representations of Gaussian Random Fields and Approximation of Elliptic PDEs with Lognormal Coefficients

Markus Bachmayr, Albert Cohen and Giovanni Migliorati
Journal of Fourier Analysis and Applications 24 (3) 621 (2018)
DOI: 10.1007/s00041-017-9539-5
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

Quasi–Monte Carlo integration with product weights for elliptic PDEs with log-normal coefficients

Yoshihito Kazashi
IMA Journal of Numerical Analysis 39 (3) 1563 (2019)
DOI: 10.1093/imanum/dry028
See this article

Multilevel quasi-Monte Carlo integration with product weights for elliptic PDEs with lognormal coefficients

L. Herrmann and C. Schwab
ESAIM: Mathematical Modelling and Numerical Analysis 53 (5) 1507 (2019)
DOI: 10.1051/m2an/2019016
See this article

MDFEM: Multivariate decomposition finite element method for elliptic PDEs with uniform random diffusion coefficients using higher-order QMC and FEM

Dong T. P. Nguyen and Dirk Nuyens
Numerische Mathematik 148 (3) 633 (2021)
DOI: 10.1007/s00211-021-01212-9
See this article

Monte Carlo and Quasi-Monte Carlo Methods

Lukas Herrmann and Christoph Schwab
Springer Proceedings in Mathematics & Statistics, Monte Carlo and Quasi-Monte Carlo Methods 241 313 (2018)
DOI: 10.1007/978-3-319-91436-7_17
See this article

A Data-Driven Approach for Multiscale Elliptic PDEs with Random Coefficients Based on Intrinsic Dimension Reduction

Sijing Li, Zhiwen Zhang and Hongkai Zhao
Multiscale Modeling & Simulation 18 (3) 1242 (2020)
DOI: 10.1137/19M1277485
See this article

Stable splittings of Hilbert spaces of functions of infinitely many variables

Michael Griebel and Peter Oswald
Journal of Complexity 41 126 (2017)
DOI: 10.1016/j.jco.2017.01.003
See this article

Uncertainty Quantification for Low-Frequency, Time-Harmonic Maxwell Equations with Stochastic Conductivity Models

Dimitris Kamilis and Nick Polydorides
SIAM/ASA Journal on Uncertainty Quantification 6 (4) 1295 (2018)
DOI: 10.1137/17M1156010
See this article

Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances

Markus Bachmayr, Ivan G. Graham, Van Kien Nguyen and Robert Scheichl
SIAM Journal on Numerical Analysis 58 (5) 2953 (2020)
DOI: 10.1137/19M1269877
See this article

Sparse Compression of Expected Solution Operators

Michael Feischl and Daniel Peterseim
SIAM Journal on Numerical Analysis 58 (6) 3144 (2020)
DOI: 10.1137/20M132571X
See this article

Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs

Markus Bachmayr, Albert Cohen, Dinh Du͂ng and Christoph Schwab
SIAM Journal on Numerical Analysis 55 (5) 2151 (2017)
DOI: 10.1137/17M111626X
See this article

Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)

Oliver G. Ernst, Björn Sprungk and Lorenzo Tamellini
SIAM Journal on Numerical Analysis 56 (2) 877 (2018)
DOI: 10.1137/17M1123079
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

Sparse quadrature for high-dimensional integration with Gaussian measure

Peng Chen
ESAIM: Mathematical Modelling and Numerical Analysis 52 (2) 631 (2018)
DOI: 10.1051/m2an/2018012
See this article

Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

Albert Cohen and Giovanni Migliorati
Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan 233 (2018)
DOI: 10.1007/978-3-319-72456-0_12
See this article

QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights

Lukas Herrmann and Christoph Schwab
Numerische Mathematik 141 (1) 63 (2019)
DOI: 10.1007/s00211-018-0991-1
See this article

On the stable sampling rate for binary measurements and wavelet reconstruction

A.C. Hansen and L. Thesing
Applied and Computational Harmonic Analysis 48 (2) 630 (2020)
DOI: 10.1016/j.acha.2018.08.004
See this article

Sparse Polynomial Chaos expansions using variational relevance vector machines

Panagiotis Tsilifis, Iason Papaioannou, Daniel Straub and Fabio Nobile
Journal of Computational Physics 416 109498 (2020)
DOI: 10.1016/j.jcp.2020.109498
See this article

Linear Reconstructions and the Analysis of the Stable Sampling Rate

Laura Thesing and Anders Hansen
Sampling Theory in Signal and Image Processing 17 (1) 103 (2018)
DOI: 10.1007/BF03549616
See this article

Intrusive generalized polynomial chaos with asynchronous time integration for the solution of the unsteady Navier–Stokes equations

P. Bonnaire, P. Pettersson and C.F. Silva
Computers & Fluids 223 104952 (2021)
DOI: 10.1016/j.compfluid.2021.104952
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

Robert Calderbank, Anders Hansen, Bogdan Roman and Laura Thesing
97 (2019)
DOI: 10.1007/978-3-319-73074-5_3
See this article

Deep Learning in High Dimension: Neural Network Expression Rates for Analytic Functions in \(\pmb{L^2(\mathbb{R}^d,\gamma_d)}\)

Christoph Schwab and Jakob Zech
SIAM/ASA Journal on Uncertainty Quantification 11 (1) 199 (2023)
DOI: 10.1137/21M1462738
See this article

MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM

Dong T. P. Nguyen and Dirk Nuyens
ESAIM: Mathematical Modelling and Numerical Analysis 55 (4) 1461 (2021)
DOI: 10.1051/m2an/2021029
See this article

On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion

Martin Eigel, Oliver G. Ernst, Björn Sprungk and Lorenzo Tamellini
SIAM Journal on Numerical Analysis 60 (2) 659 (2022)
DOI: 10.1137/20M1364722
See this article

Multilevel representations of isotropic Gaussian random fields on the sphere

Markus Bachmayr and Ana Djurdjevac
IMA Journal of Numerical Analysis (2022)
DOI: 10.1093/imanum/drac034
See this article

Goal-oriented adaptive finite element multilevel Monte Carlo with convergence rates

Joakim Beck, Yang Liu, Erik von Schwerin and Raúl Tempone
Computer Methods in Applied Mechanics and Engineering 402 115582 (2022)
DOI: 10.1016/j.cma.2022.115582
See this article

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

The uniform sparse FFT with application to PDEs with random coefficients

Lutz Kämmerer, Daniel Potts and Fabian Taubert
Sampling Theory, Signal Processing, and Data Analysis 20 (2) (2022)
DOI: 10.1007/s43670-022-00037-3
See this article