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swMATH10167MaRDI QIDQ22135

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Related Items (67)

A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data ⋮ An adaptive hp-version stochastic Galerkin method for constrained optimal control problem governed by random reaction diffusion equations ⋮ Adaptive stochastic Galerkin FEM with hierarchical tensor representations ⋮ Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion ⋮ Error Estimation and Adaptivity for Stochastic Collocation Finite Elements Part II: Multilevel Approximation ⋮ An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality ⋮ Hyperbolicity-preserving and well-balanced stochastic Galerkin method for two-dimensional shallow water equations ⋮ Error Estimation and Adaptivity for Stochastic Collocation Finite Elements Part I: Single-Level Approximation ⋮ A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes ⋮ CBS constants \& their role in error estimation for stochastic Galerkin finite element methods ⋮ Large deformation shape uncertainty quantification in acoustic scattering ⋮ Rank Bounds for Approximating Gaussian Densities in the Tensor-Train Format ⋮ Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format ⋮ Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems ⋮ An Adaptive Multilevel Monte Carlo Method with Stochastic Bounds for Quantities of Interest with Uncertain Data ⋮ Local Equilibration Error Estimators for Guaranteed Error Control in Adaptive Stochastic Higher-Order Galerkin Finite Element Methods ⋮ Interpolatory tensorial reduced order models for parametric dynamical systems ⋮ Adaptive quasi-Monte Carlo finite element methods for parametric elliptic PDEs ⋮ Particle number conservation and block structures in matrix product states ⋮ Towards Provably Robust Watermarking ⋮ A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method ⋮ On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion ⋮ Enhanced alternating energy minimization methods for stochastic Galerkin matrix equations ⋮ Approximating Optimal feedback Controllers of Finite Horizon Control Problems Using Hierarchical Tensor Formats ⋮ Multilevel tensor approximation of PDEs with random data ⋮ Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations ⋮ Computable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic Data ⋮ An Efficient Reduced Basis Solver for Stochastic Galerkin Matrix Equations ⋮ A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case ⋮ Numerical upscaling of parametric microstructures in a possibilistic uncertainty framework with tensor trains ⋮ An overview on deep learning-based approximation methods for partial differential equations ⋮ A sparse FFT approach for ODE with random coefficients ⋮ T-IFISS: a toolbox for adaptive FEM computation ⋮ Adaptive stochastic Galerkin FEM ⋮ Robust Preconditioning for Stochastic Galerkin Formulations of Parameter-Dependent Nearly Incompressible Elasticity Equations ⋮ Hyperbolic stochastic Galerkin formulation for the \(p\)-system ⋮ Robust a posteriori error estimation for parameter-dependent linear elasticity equations ⋮ Sampling-free Bayesian inversion with adaptive hierarchical tensor representations ⋮ Geometric Methods on Low-Rank Matrix and Tensor Manifolds ⋮ Efficient Reduced Basis Methods for Saddle Point Problems with Applications in Groundwater Flow ⋮ Adaptive algorithm for stochastic Galerkin method. ⋮ Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations ⋮ Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs ⋮ Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations ⋮ Covariance regularity and \(\mathcal {H}\)-matrix approximation for rough random fields ⋮ Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients ⋮ Hierarchical preconditioning for the stochastic Galerkin method: upper bounds to the strengthened CBS constants ⋮ Efficient Adaptive Stochastic Galerkin Methods for Parametric Operator Equations ⋮ An Optimal Solver for Linear Systems Arising from Stochastic FEM Approximation of Diffusion Equations with Random Coefficients ⋮ An adaptive multilevel Monte Carlo algorithm for the stochastic drift-diffusion-Poisson system ⋮ Spatio-stochastic adaptive discontinuous Galerkin methods ⋮ A posteriori error estimation for elliptic partial differential equations with small uncertainties ⋮ Block Preconditioning of Stochastic Galerkin Problems: New Two-sided Guaranteed Spectral Bounds ⋮ Approximation and sampling of multivariate probability distributions in the tensor train decomposition ⋮ Variational Monte Carlo -- bridging concepts of machine learning and high-dimensional partial differential equations ⋮ Tensor train approximation of moment equations for elliptic equations with lognormal coefficient ⋮ Accelerating Monte Carlo estimation with derivatives of high-level finite element models ⋮ A Hybrid Alternating Least Squares--TT-Cross Algorithm for Parametric PDEs ⋮ A Bramble--Pasciak Conjugate Gradient Method for Discrete Stokes Equations with Random Viscosity ⋮ Non-intrusive tensor reconstruction for high-dimensional random PDEs ⋮ Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations ⋮ Adaptive low-rank approximations for operator equations: Accuracy control and computational complexity ⋮ Parameter-Robust Stochastic Galerkin Mixed Approximation for Linear Poroelasticity with Uncertain Inputs ⋮ A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients ⋮ Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations ⋮ The uniform sparse FFT with application to PDEs with random coefficients ⋮ SDE Based Regression for Linear Random PDEs

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