Sparse polynomial approximations for affine parametric saddle point problems (Q2679763)

scientific article; zbMATH DE number 7644540

Language	Label	Description	Also known as
English	Sparse polynomial approximations for affine parametric saddle point problems	scientific article; zbMATH DE number 7644540

Statements

instance of

scholarly article

0 references

title

Sparse polynomial approximations for affine parametric saddle point problems (English)

0 references

0 references

0 references

Vietnam Journal of Mathematics

0 references

publication date

23 January 2023

0 references

full work available at URL

https://arxiv.org/abs/1809.10251

0 references

zbMATH Keywords

sparse polynomial approximation

0 references

saddle point problems

0 references

parametric PDEs

0 references

dimension-independent convergence

0 references

MaRDI profile type

Publication

0 references

cites work

A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

0 references

Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations

0 references

Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients

0 references

Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients

0 references

Model Reduction and Approximation

0 references

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

0 references

Convergence Rates for Greedy Algorithms in Reduced Basis Methods

0 references

Mixed Finite Element Methods and Applications

0 references

Reduced basis techniques for stochastic problems

0 references

\textit{A priori} convergence of the greedy algorithm for the parametrized reduced basis method

0 references

Sparse quadrature for high-dimensional integration with Gaussian measure

0 references

Weighted Reduced Basis Method for Stochastic Optimal Control Problems with Elliptic PDE Constraint

0 references

A new algorithm for high-dimensional uncertainty quantification based on dimension-adaptive sparse grid approximation and reduced basis methods

0 references

Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations

0 references

Reduced Basis Methods for Uncertainty Quantification

0 references

Sparse-grid, reduced-basis Bayesian inversion

0 references

Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems

0 references

Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs

0 references

Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs

0 references

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

0 references

High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs

0 references

Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients

0 references

Approximation of high-dimensional parametric PDEs

0 references

Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs

0 references

ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S

0 references

Multivariate Approximation in Downward Closed Polynomial Spaces

0 references

A non-adapted sparse approximation of PDEs with stochastic inputs

0 references

Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)

0 references

Computational Higher Order Quasi-Monte Carlo Integration

0 references

Dimension-adaptive tensor-product quadrature

0 references

Q3997987

0 references

Multi-index Monte Carlo: when sparsity meets sampling

0 references

Analyticity in infinite dimensional spaces

0 references

Korn’s Inequalities and Their Applications in Continuum Mechanics

0 references

Analytic regularity and GPC approximation for control problems constrained by linear parametric elliptic and parabolic PDEs

0 references

Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients

0 references

A theoretical analysis of deep neural networks and parametric PDEs

0 references

A Christoffel function weighted least squares algorithm for collocation approximations

0 references

A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data

0 references

Derivative-informed projected neural networks for high-dimensional parametric maps governed by PDEs

0 references

Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations

0 references

Sparse, adaptive Smolyak quadratures for Bayesian inverse problems

0 references

Karhunen-Loève approximation of random fields by generalized fast multipole methods

0 references

Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ

0 references

Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients

0 references

High-Order Collocation Methods for Differential Equations with Random Inputs

0 references

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

0 references

Some observations on Babuška and Brezzi theories

0 references

Convergence rates of high dimensional Smolyak quadrature

0 references

Identifiers

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

0 references

0 references

10.1007/S10013-022-00584-1

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:2679763