Sparse polynomial approximations for affine parametric saddle point problems
From MaRDI portal
Publication:2679763
DOI10.1007/s10013-022-00584-1OpenAlexW2893041993MaRDI QIDQ2679763
Publication date: 23 January 2023
Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.10251
saddle point problemsparametric PDEssparse polynomial approximationdimension-independent convergence
Error bounds for boundary value problems involving PDEs (65N15) Multidimensional problems (41A63) Approximation by polynomials (41A10) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)
Cites Work
- Unnamed Item
- Multi-index Monte Carlo: when sparsity meets sampling
- Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations
- Reduced basis techniques for stochastic problems
- High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs
- Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
- Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
- A non-adapted sparse approximation of PDEs with stochastic inputs
- Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
- Analyticity in infinite dimensional spaces
- Some observations on Babuška and Brezzi theories
- Dimension-adaptive tensor-product quadrature
- Derivative-informed projected neural networks for high-dimensional parametric maps governed by PDEs
- A theoretical analysis of deep neural networks and parametric PDEs
- Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems
- A new algorithm for high-dimensional uncertainty quantification based on dimension-adaptive sparse grid approximation and reduced basis methods
- Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients
- Karhunen-Loève approximation of random fields by generalized fast multipole methods
- Sparse-grid, reduced-basis Bayesian inversion
- Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs
- A prioriconvergence of the Greedy algorithm for the parametrized reduced basis method
- Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs
- Sparse, adaptive Smolyak quadratures for Bayesian inverse problems
- Weighted Reduced Basis Method for Stochastic Optimal Control Problems with Elliptic PDE Constraint
- Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations
- Computational Higher Order Quasi-Monte Carlo Integration
- Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients
- Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients
- A Christoffel function weighted least squares algorithm for collocation approximations
- ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
- Convergence Rates for Greedy Algorithms in Reduced Basis Methods
- A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- Model Reduction and Approximation
- Multivariate Approximation in Downward Closed Polynomial Spaces
- Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ
- Reduced Basis Methods for Uncertainty Quantification
- Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)
- Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
- Korn’s Inequalities and Their Applications in Continuum Mechanics
- Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients
- Mixed Finite Element Methods and Applications
- Sparse quadrature for high-dimensional integration with Gaussian measure
- Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations
- Convergence rates of high dimensional Smolyak quadrature
- Approximation of high-dimensional parametric PDEs
- Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs
- High-Order Collocation Methods for Differential Equations with Random Inputs
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data