Efficient Adaptive Algorithms for Elliptic PDEs with Random Data

DOI10.1137/17M1139928zbMath1398.65289OpenAlexW2794203769MaRDI QIDQ4636373

Leonardo Rocchi, Alexei Bespalov

Publication date: 19 April 2018

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

Full work available at URL: https://doi.org/10.1137/17m1139928

zbMATH Keywords

singularitiesadaptive methodsa posteriori error estimationstochastic finite elementsstochastic Galerkin methodsPDEs with random data

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) 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) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (11)

Error Estimation and Adaptivity for Stochastic Collocation Finite Elements Part I: Single-Level Approximation ⋮ CBS constants \& their role in error estimation for stochastic Galerkin finite element methods ⋮ Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs ⋮ A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case ⋮ T-IFISS: a toolbox for adaptive FEM computation ⋮ Robust a posteriori error estimation for parameter-dependent linear elasticity equations ⋮ Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs ⋮ Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method ⋮ T-IFISS ⋮ Efficient Adaptive Multilevel Stochastic Galerkin Approximation Using Implicit A Posteriori Error Estimation ⋮ Convergence of Adaptive Stochastic Galerkin FEM

Cites Work

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• Adaptive stochastic Galerkin FEM
• Adaptive finite element methods with convergence rates
• A recursive approach to local mesh refinement in two and three dimensions
• Adaptive stochastic Galerkin FEM with hierarchical tensor representations
• Finite Elements and Fast Iterative Solvers
• Energy Norm A Posteriori Error Estimation for Parametric Operator Equations
• Mathematically Founded Design of Adaptive Finite Element Software
• An Introduction to Computational Stochastic PDEs
• Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs
• Local Equilibration Error Estimators for Guaranteed Error Control in Adaptive Stochastic Higher-Order Galerkin Finite Element Methods
• A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes
• Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
• Mesh Refinement Processes Based on the Generalized Bisection of Simplices
• The Role of the Strengthened Cauchy–Buniakowskii–Schwarz Inequality in Multilevel Methods
• Local mesh refinement in 2 and 3 dimensions
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Efficient Adaptive Stochastic Galerkin Methods for Parametric Operator Equations

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