Explicit cost bounds of stochastic Galerkin approximations for parameterized PDEs with random coefficients

DOI10.1016/j.camwa.2015.12.005zbMath1443.65200arXiv1507.05545OpenAlexW1464641790MaRDI QIDQ2007265

Clayton G. Webster, Guannan Zhang, Nick C. Dexter

Publication date: 12 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.05545

zbMATH Keywords

finite elementscomplexity analysisstochastic collocationstochastic Galerkinexplicit cost boundssparse polynomial approximation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Related Items (1)

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

Uses Software

• DistMesh

Cites Work

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• Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
• Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
• A method for numerical integration on an automatic computer
• On asymptotics and estimates for the uniform norms of the Lagrange interpolation polynomials corresponding to the Chebyshev nodal points
• Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
• Iterative solution of systems of linear equations arising in the context of stochastic finite elements
• Computational aspects of the stochastic finite element method
• On Leja sequences: some results and applications
• Efficient Iterative Solvers for Stochastic Galerkin Discretizations of Log-Transformed Random Diffusion Problems
• Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison
• Stochastic Galerkin Matrices
• ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
• A Kronecker Product Preconditioner for Stochastic Galerkin Finite Element Discretizations
• ASSESSMENT OF COLLOCATION AND GALERKIN APPROACHES TO LINEAR DIFFUSION EQUATIONS WITH RANDOM DATA
• Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients
• Block-diagonal preconditioning for spectral stochastic finite-element systems
• 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
• Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients
• A Simple Mesh Generator in MATLAB
• Stochastic finite element methods for partial differential equations with random input data
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• An Adaptive Wavelet Stochastic Collocation Method for Irregular Solutions of Partial Differential Equations with Random Input Data
• Theoretical Numerical Analysis

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