Error Decomposition and Adaptivity for Response Surface Approximations from PDEs with Parametric Uncertainty

DOI10.1137/140962632zbMath1327.65011OpenAlexW2180064962MaRDI QIDQ3452534

No author found.

Publication date: 12 November 2015

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/140962632

zbMATH Keywords

adaptivitya posteriori error analysisadjoint problemerror decompositionstochastic spectral methods

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (9)

Convergence of Probability Densities Using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification ⋮ Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs ⋮ A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws ⋮ Goal-oriented adaptive surrogate construction for stochastic inversion ⋮ Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs ⋮ Spatio-stochastic adaptive discontinuous Galerkin methods ⋮ Probabilistic modeling and global sensitivity analysis for CO\(_2\) storage in geological formations: a spectral approach ⋮ Goal-oriented error control of stochastic system approximations using metric-based anisotropic adaptations ⋮ Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations

Cites Work

• Unnamed Item
• Unnamed Item
• Uncertainty propagation using Wiener-Haar expansions
• Multi-resolution analysis of Wiener-type uncertainty propagation schemes
• Solution verification, goal-oriented adaptive methods for stochastic advection-diffusion problems
• Sparse pseudospectral approximation method
• An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
• On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors
• Sparse grid collocation schemes for stochastic natural convection problems
• Dual-based a posteriori error estimate for stochastic finite element methods
• An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
• Beyond Wiener-Askey expansions: handling arbitrary PDFs
• A Posteriori Error Analysis of Parameterized Linear Systems Using Spectral Methods
• A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions
• Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
• An optimal control approach to a posteriori error estimation in finite element methods
• Nonparametric Density Estimation for Randomly Perturbed Elliptic Problems I: Computational Methods, A Posteriori Analysis, and Adaptive Error Control
• 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
• A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations
• Estimating the error of numerical solutions of systems of reaction-diffusion equations
• Global error control for the continuous Galerkin finite element method for ordinary differential equations
• Probability Theory with Applications
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

This page was built for publication: Error Decomposition and Adaptivity for Response Surface Approximations from PDEs with Parametric Uncertainty