Towards a unified multiresolution scheme for treating discontinuities in differential equations with uncertainties

DOI10.1016/j.matcom.2016.02.002OpenAlexW2286412266MaRDI QIDQ2229096

Pietro Marco Congedo, Gianluca Geraci, Remi Abgrall

Publication date: 19 February 2021

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2016.02.002

zbMATH Keywords

heat equationfinite elementdifferential equationsmultiresolutionuncertainty quantification

Mathematics Subject Classification ID

Stochastic analysis (60Hxx) Probabilistic methods, stochastic differential equations (65Cxx)

Related Items (1)

A novel weakly-intrusive non-linear multiresolution framework for uncertainty quantification in hyperbolic partial differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A novel weakly-intrusive non-linear multiresolution framework for uncertainty quantification in hyperbolic partial differential equations
• A one-time truncate and encode multiresolution stochastic framework
• Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
• Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
• Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids
• Uncertainty propagation using Wiener-Haar expansions
• Multi-resolution analysis of Wiener-type uncertainty propagation schemes
• Time-dependent generalized polynomial chaos
• Stochastic discrete equation method (SDEM) for two-phase flows
• Nonlinear Harten's multiresolution on the quincunx pyramid
• Multi-element probabilistic collocation method in high dimensions
• Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
• Long-term behavior of polynomial chaos in stochastic flow simulations
• Discontinuity detection in multivariate space for stochastic simulations
• An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
• Numerical integration using sparse grids
• High resolution schemes for hyperbolic conservation laws. (Reprint)
• Dimension-adaptive tensor-product quadrature
• Modeling uncertainty in flow simulations via generalized polynomial chaos.
• Sparse grid collocation schemes for stochastic natural convection problems
• Sparse Tensor Discretization of Elliptic sPDEs
• A Sparse Composite Collocation Finite Element Method for Elliptic SPDEs.
• Multilevel Monte Carlo Path Simulation
• Spectral Methods for Uncertainty Quantification
• Multiresolution Representation in Unstructured Meshes
• Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I
• Multiresolution algorithms for the numerical solution of hyperbolic conservation laws
• Multiresolution Representation of Data: A General Framework
• High-Order Collocation Methods for Differential Equations with Random Inputs
• On the distribution of points in a cube and the approximate evaluation of integrals
• The Homogeneous Chaos
• The Monte Carlo Method
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

This page was built for publication: Towards a unified multiresolution scheme for treating discontinuities in differential equations with uncertainties