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A Convergent Adaptive Finite Element Stochastic Galerkin Method Based on Multilevel Expansions of Random Fields
Markus Bachmayr, Martin Eigel, Henrik Eisenmann and Igor Voulis SIAM Journal on Numerical Analysis 63(4) 1776 (2025) https://doi.org/10.1137/24M1649253
Adaptive refinement in incompressible fluid flow simulation based on THB-splines-powered isogeometric analysis
A Posteriori Error Estimates for the Crank–Nicolson Method: Application to Parabolic Partial Differential Equations Subject to a Robin Boundary Condition with Small Randomness
Representative Volume Element Approximations in Elastoplastic Spring Networks
Sabine Haberland, Patrick Jaap, Stefan Neukamm, Oliver Sander and Mario Varga Multiscale Modeling & Simulation 22(1) 588 (2024) https://doi.org/10.1137/23M156656X
Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM
Error Estimation and Adaptivity for Stochastic Collocation Finite Elements Part I: Single-Level Approximation
Alex Bespalov, David J. Silvester and Feng Xu SIAM Journal on Scientific Computing 44(5) A3393 (2022) https://doi.org/10.1137/21M1446745
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) https://doi.org/10.1137/20M1364722
An adaptive hp-version stochastic Galerkin method for constrained optimal control problem governed by random reaction diffusion equations
Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method
Alex Bespalov, Dirk Praetorius and Michele Ruggeri SIAM/ASA Journal on Uncertainty Quantification 9(3) 1184 (2021) https://doi.org/10.1137/20M1342586
Sparse Grids and Applications - Munich 2018
Fabio Nobile and Eva Vidličková Lecture 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
Convergence of adaptive stochastic collocation with finite elements
Non-intrusive Tensor Reconstruction for High-Dimensional Random PDEs
Martin Eigel, Johannes Neumann, Reinhold Schneider and Sebastian Wolf Computational Methods in Applied Mathematics 19(1) 39 (2019) https://doi.org/10.1515/cmam-2018-0028
Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs
Alex Bespalov, Dirk Praetorius, Leonardo Rocchi and Michele Ruggeri Computer Methods in Applied Mechanics and Engineering 345 951 (2019) https://doi.org/10.1016/j.cma.2018.10.041
Variational Monte Carlo—bridging concepts of machine learning and high-dimensional partial differential equations
Martin Eigel, Reinhold Schneider, Philipp Trunschke and Sebastian Wolf Advances in Computational Mathematics 45(5-6) 2503 (2019) https://doi.org/10.1007/s10444-019-09723-8
Parametric PDEs: sparse or low-rank approximations?