Convergence rate for the ordered upwind method

DOI10.1007/s10915-016-0163-3zbMath1354.65139arXiv1601.02885OpenAlexW3103447624MaRDI QIDQ333193

Alex Shum, Amir Khajepour, Kirsten A. Morris

Publication date: 28 October 2016

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.02885

zbMATH Keywords

Hamilton-Jacobi-Bellman equationviscosity solutionnumerical exampleserror boundconvergence rateanisotropic optimal controlordered upwind methods

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Existence theories for optimal control problems involving partial differential equations (49J20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Discrete approximations in optimal control (49M25)

Related Items

Neighbor-gradient single-pass method for solving anisotropic eikonal equation, Controlling mean exit time of stochastic dynamical systems based on quasipotential and machine learning, Riemannian Fast-Marching on Cartesian Grids, Using Voronoi's First Reduction of Quadratic Forms

Cites Work

• Unnamed Item
• Unnamed Item
• A note on two problems in connexion with graphs
• Estimation of reactive fluxes in gradient stochastic systems using an analogy with electric circuits
• A Hamilton-Jacobi framework for modeling folds in structural geology
• A fast marching method for Hamilton-Jacobi equations modeling monotone front propagations
• Approximation schemes for viscosity solutions of Hamilton-Jacobi equations
• Discrete time high-order schemes for viscosity solutions of Hamilton- Jacobi-Bellman equations
• An ordered upwind method with precomputed stencil and monotone node acceptance for solving static convex Hamilton-Jacobi equations
• An Efficient Method for Multiobjective Optimal Control and Optimal Control Subject to Integral Constraints
• Two Approximations of Solutions of Hamilton-Jacobi Equations
• On Deterministic Control Problems: An Approximation Procedure for the Optimal Cost I. The Stationary Problem
• Computing geodesic paths on manifolds
• Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms
• Ordered upwind methods for static Hamilton–Jacobi equations
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
• High order numerical discretization for Hamilton-Jacobi equations on triangular meshes.