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

DOI10.1137/17M1123079OpenAlexW2606283473WikidataQ130039823 ScholiaQ130039823MaRDI QIDQ4637512

Oliver G. Ernst, Björn Sprungk, Lorenzo Tamellini

Publication date: 24 April 2018

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.07239

zbMATH Keywords

sparse gridshigh-dimensional interpolationhigh-dimensional approximationparametric PDEsstochastic collocationrandom PDEsbest-\(N\)-term approximationGauss-Hermite pointslognormal diffusion coefficient

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Numerical interpolation (65D05) Numerical solutions to stochastic differential and integral equations (65C30) Algorithms for approximation of functions (65D15)

Related Items (14)

On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion ⋮ IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains ⋮ Uncertainty quantification analysis in discrete fracture network flow simulations ⋮ Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs ⋮ Sparse polynomial approximations for affine parametric saddle point problems ⋮ Collocation approximation by deep neural ReLU networks for parametric and stochastic PDEs with lognormal inputs ⋮ Numerical smoothing with hierarchical adaptive sparse grids and quasi-Monte Carlo methods for efficient option pricing ⋮ Uncertainty Quantification for Low-Frequency, Time-Harmonic Maxwell Equations with Stochastic Conductivity Models ⋮ Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs) ⋮ Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs ⋮ Domain Uncertainty Quantification in Computational Electromagnetics ⋮ Sparse quadrature for high-dimensional integration with Gaussian measure ⋮ On expansions and nodes for sparse grid collocation of lognormal elliptic PDEs ⋮ PDE-Constrained Optimal Control Problems with Uncertain Parameters using SAGA

Uses Software

• PATSYM
• HRMSYM

Cites Work

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• Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: Application to random elliptic PDEs
• High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs
• Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
• Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity
• Global sensitivity analysis through polynomial chaos expansion of a basin-scale geochemical compaction model
• Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
• Sparse pseudospectral approximation method
• Mean convergence of Lagrange interpolation. II
• Dimension-adaptive tensor-product quadrature
• Elliptic partial differential equations of second order
• Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight
• On the Lebesgue constant of Leja sequences for the complex unit disk and of their real projection
• On Leja sequences: some results and applications
• An Adaptive Sparse Grid Algorithm for Elliptic PDEs with Lognormal Diffusion Coefficient
• Sparse, adaptive Smolyak quadratures for Bayesian inverse problems
• Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients
• Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients
• Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients
• Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison
• Approximating Infinity-Dimensional Stochastic Darcy's Equations without Uniform Ellipticity
• ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
• Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs
• Spectral Methods for Uncertainty Quantification
• A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)
• Sparse quadrature for high-dimensional integration with Gaussian measure
• Adaptive Leja Sparse Grid Constructions for Stochastic Collocation and High-Dimensional Approximation
• Approximation of high-dimensional parametric PDEs
• STOCHASTIC GALERKIN DISCRETIZATION OF THE LOG-NORMAL ISOTROPIC DIFFUSION PROBLEM
• On the convergence of the stochastic Galerkin method for random elliptic partial differential equations
• N-TERM WIENER CHAOS APPROXIMATION RATES FOR ELLIPTIC PDEs WITH LOGNORMAL GAUSSIAN RANDOM INPUTS
• High-Order Collocation Methods for Differential Equations with Random Inputs
• A Quasi-optimal Sparse Grids Procedure for Groundwater Flows
• On the Lebesgue constant of weighted Leja points for Lagrange interpolation on unbounded domains
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

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