Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method
From MaRDI portal
Publication:5158920
DOI10.1137/20M1342586MaRDI QIDQ5158920
Michele Ruggeri, Dirk Praetorius, Alexei Bespalov
Publication date: 26 October 2021
Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2006.02255
finite element methodadaptive methodsa posteriori error analysisparametric PDEstwo-level error estimationmultilevel stochastic Galerkin method
Probabilistic models, generic numerical methods in probability and statistics (65C20) 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) PDEs with randomness, stochastic partial differential equations (35R60) Numerical analysis (65-XX)
Related Items
Error Estimation and Adaptivity for Stochastic Collocation Finite Elements Part II: Multilevel Approximation, Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs, Two-level error estimation for the integral fractional Laplacian, Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots
Cites Work
- Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats
- On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection
- Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
- Adaptive stochastic Galerkin FEM
- Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
- Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations
- Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs
- Optimal convergence behavior of adaptive FEM driven by simple \((h-h/2)\)-type error estimators
- A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data
- 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
- The saturation assumption yields optimal convergence of two-level adaptive BEM
- Non-intrusive tensor reconstruction for high-dimensional random PDEs
- Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients
- Numerical solution of spectral stochastic finite element systems
- 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
- An Optimal Iterative Solver for Symmetric Indefinite Systems Stemming from Mixed Approximation
- 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
- 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
- Hierarchical Tensor Approximation of Output Quantities of Parameter-Dependent PDEs
- A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format
- Block-diagonal preconditioning for spectral stochastic finite-element systems
- Adaptive Multilevel Monte Carlo Methods for Stochastic Variational Inequalities
- Efficient Adaptive Algorithms for Elliptic PDEs with Random Data
- Stochastic finite element methods for partial differential equations with random input data
- A Convergent Adaptive Algorithm for Poisson’s Equation
- A Posteriori Error Estimates for Elliptic Problems in Two and Three Space Dimensions
- To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case
- Efficient Adaptive Multilevel Stochastic Galerkin Approximation Using Implicit A Posteriori Error Estimation
- Convergence of Adaptive Stochastic Galerkin FEM
- The completion of locally refined simplicial partitions created by bisection
- Efficient Adaptive Stochastic Galerkin Methods for Parametric Operator Equations
