Error Estimation and Adaptivity for Stochastic Collocation Finite Elements Part II: Multilevel Approximation
DOI10.1137/22M1479361MaRDI QIDQ5889352
David J. Silvester, Alexei Bespalov
Publication date: 20 April 2023
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2202.08902
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) PDEs with randomness, stochastic partial differential equations (35R60) Numerical analysis (65-XX)
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Cites Work
- Adaptive stochastic Galerkin FEM
- Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
- Convergence of adaptive stochastic collocation with finite elements
- A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data
- Multi-index stochastic collocation for random PDEs
- Convergence Rates of Multilevel and Sparse Tensor Approximations for a Random Elliptic PDE
- A Sparse Composite Collocation Finite Element Method for Elliptic SPDEs.
- A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method
- Adaptive Multilevel Monte Carlo Methods for Stochastic Variational Inequalities
- Error Estimation and Adaptivity for Stochastic Collocation Finite Elements Part I: Single-Level Approximation
- On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion
- Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM
- Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method
- Efficient Adaptive Multilevel Stochastic Galerkin Approximation Using Implicit A Posteriori Error Estimation
- Efficient Adaptive Stochastic Galerkin Methods for Parametric Operator Equations
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
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