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## Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients

ESAIM: M2AN, 51 1 (2017) 341-363

## 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

## 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

## Near-optimal approximation methods for elliptic PDEs with lognormal coefficients

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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## Sparse Compression of Expected Solution Operators

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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

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

## 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

## 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

## 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

## 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

## 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

## 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