An adaptive sparse grid local discontinuous Galerkin method for Hamilton-Jacobi equations in high dimensions
type: Item
instance of: scholarly article
title: An adaptive sparse grid local discontinuous Galerkin method for Hamilton-Jacobi equations in high dimensions
author: Wei Guo
author: Juntao Huang
author: Zhanjing Tao
author: Yingda Cheng
published in: Journal of Computational Physics
publication date: 2022-04-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/2006.05250
Mathematics Subject Classification ID: 65Mxx
Mathematics Subject Classification ID: 35Fxx
Mathematics Subject Classification ID: 35Lxx
zbMATH DE Number: 7513855
zbMATH Keywords: sparse grid
zbMATH Keywords: adaptivity
zbMATH Keywords: local discontinuous Galerkin
zbMATH Keywords: Hamilton-Jacobi equations
zbMATH Keywords: high dimensions
MaRDI profile type: Publication
OpenAlex ID: W3035286161
cites work: Numerical discretization of the first-order Hamilton-Jacobi equation on triangular meshes
cites work: A Class of Bases in $L^2$ for the Sparse Representation of Integral Operators
cites work: An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations
cites work: Sparse grids
cites work: A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
cites work: A new discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
cites work: Algorithm for overcoming the curse of dimensionality for time-dependent non-convex Hamilton-Jacobi equations arising from optimal control and differential games problems
cites work: Algorithm for overcoming the curse of dimensionality for state-dependent Hamilton-Jacobi equations
cites work: The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
cites work: The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
cites work: Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
cites work: Viscosity Solutions of Hamilton-Jacobi Equations
cites work: Two Approximations of Solutions of Hamilton-Jacobi Equations
cites work: Overcoming the curse of dimensionality for some Hamilton-Jacobi partial differential equations via neural network architectures
cites work: Algorithms for overcoming the curse of dimensionality for certain Hamilton-Jacobi equations arising in control theory and elsewhere
cites work: Q5189317
cites work: Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids
cites work: A sparse grid discontinuous Galerkin method for high-dimensional transport equations and its application to kinetic simulations
cites work: An Adaptive Multiresolution Discontinuous Galerkin Method for Time-Dependent Transport Equations in Multidimensions
cites work: Local-structure-preserving discontinuous Galerkin methods with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations
cites work: Solving high-dimensional partial differential equations using deep learning
cites work: A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
cites work: An adaptive multiresolution interior penalty discontinuous Galerkin method for wave equations in second order form
cites work: Error estimates to smooth solutions of semi‐discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws
cites work: Weighted ENO Schemes for Hamilton--Jacobi Equations
cites work: Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equations
cites work: An alternative formulation of discontinous Galerkin schemes for solving Hamilton-Jacobi equations
cites work: HJB-POD-Based Feedback Design for the Optimal Control of Evolution Problems
cites work: High order two dimensional nonoscillatory methods for solving Hamilton-Jacobi scalar equations
cites work: Analysis of the discontinuous Galerkin method for Hamilton-Jacobi equations
cites work: A central discontinuous Galerkin method for Hamilton-Jacobi equations
cites work: Q3961832
cites work: Q4488070
cites work: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
cites work: High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations
cites work: Hermite WENO schemes for Hamilton-Jacobi equations
cites work: Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems
cites work: Mathematics and Computation in Imaging Science and Information Processing
cites work: Efficient implementation of essentially nonoscillatory shock-capturing schemes
cites work: Sparse grid discontinuous Galerkin methods for high-dimensional elliptic equations
cites work: A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equations
cites work: High-Order WENO Schemes for Hamilton--Jacobi Equations on Triangular Meshes
DOI: 10.1016/J.JCP.2021.110294
description: scientific article; zbMATH DE number 7513855