Efficient Adaptive Multilevel Stochastic Galerkin Approximation Using Implicit A Posteriori Error Estimation

DOI10.1137/18M1194420zbMath1420.65120arXiv1806.05987OpenAlexW2963604924MaRDI QIDQ5230614

Catherine E. Powell, Adam J. Crowder, Alexei Bespalov

Publication date: 28 August 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.05987

zbMATH Keywords

finite element methodsadaptivitymultilevel methodsa posteriori error estimationstochastic Galerkin approximation

Mathematics Subject Classification ID

Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items

Error Estimation and Adaptivity for Stochastic Collocation Finite Elements Part II: Multilevel Approximation ⋮ An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality ⋮ On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion ⋮ Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs ⋮ T-IFISS: a toolbox for adaptive FEM computation ⋮ Robust a posteriori error estimation for parameter-dependent linear elasticity equations ⋮ Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method ⋮ Block Preconditioning of Stochastic Galerkin Problems: New Two-sided Guaranteed Spectral Bounds ⋮ Convergence of Adaptive Stochastic Galerkin FEM ⋮ Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations ⋮ Parameter-Robust Stochastic Galerkin Mixed Approximation for Linear Poroelasticity with Uncertain Inputs ⋮ A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Uses Software

• T-IFISS

Cites Work

• Unnamed Item
• Unnamed Item
• Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
• Adaptive stochastic Galerkin FEM
• Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
• Adaptive algorithm for stochastic Galerkin method.
• Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity
• Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
• Sparse high order FEM for elliptic sPDEs
• CBS constants \& their role in error estimation for stochastic Galerkin finite element methods
• An adaptive stochastic Galerkin method for random elliptic operators
• Convergence Rates of Multilevel and Sparse Tensor Approximations for a Random Elliptic PDE
• Energy Norm A Posteriori Error Estimation for Parametric Operator Equations
• An Introduction to Computational Stochastic PDEs
• Stochastic Galerkin Matrices
• Sparse Tensor Discretization of Elliptic sPDEs
• ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
• Local Equilibration Error Estimators for Guaranteed Error Control in Adaptive Stochastic Higher-Order Galerkin Finite Element Methods
• Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients
• A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes
• A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Block-diagonal preconditioning for spectral stochastic finite-element systems
• Efficient Adaptive Algorithms for Elliptic PDEs with Random Data
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods
• Efficient Adaptive Stochastic Galerkin Methods for Parametric Operator Equations
• Solution of stochastic partial differential equations using Galerkin finite element techniques