Semi-Lagrangian schemes for Hamilton-Jacobi equations, discrete representation formulae and Godunov methods
type: Item
instance of: scholarly article
title: Semi-Lagrangian schemes for Hamilton-Jacobi equations, discrete representation formulae and Godunov methods
zbMATH Open document ID: 1007.65060
published in: Journal of Computational Physics
publication date: 2002-07-04T00:00:00Z
review text: The authors study a class of semi-Lagrangian schemes for the Hamilton-Jacobi equation of the first order, in particular, they consider the model problem: \[ v_{t}(t)+H(\nabla v(t))=0, x\in \mathbb{R}^{N}, t\in \mathbb{R}, v(x,0)=v_{0}(x), x\in \mathbb{R}^{N}. \] These schemes can be interpreted as a discrete analogue of the Hopf-Lax-Oleinik representation formula for the exact viscosity solution of the first order evaluative Hamilton-Jacobi equations. The authors study the semi-Lagrangian schemes for the Hamilton-Jacobi equation as an analogue of Godunov scheme for conservation laws and show that these schemes are strictly connected with the Hopf representation formulae for the exact solution. In the end of the paper they analyse the numerical experiments with tests for the eikonal propagation of fronts, for the strictly convex Hamiltonian and for a front evolving on a manifold.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35L45
zbMATH DE Number: 1763713
zbMATH Keywords: semi-Lagrangian schemes
zbMATH Keywords: Hamilton-Jacobi equation
zbMATH Keywords: Godunov methods
zbMATH Keywords: discrete representation
zbMATH Keywords: Hopf representation formulae
zbMATH Keywords: numerical experiments
author: M. Falcone
author: Roberto Ferretti
describes a project that uses: BRENT
MaRDI profile type: Publication
full work available at URL: jcph.2001.6954
OpenAlex ID: W2014405238
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DOI: 10.1006/JCPH.2001.6954
description: scientific article; zbMATH DE number 1763713