High order two dimensional nonoscillatory methods for solving Hamilton-Jacobi scalar equations
type: Item
instance of: scholarly article
title: High order two dimensional nonoscillatory methods for solving Hamilton-Jacobi scalar equations
zbMATH Open document ID: 0849.65075
author: F. Lafon
author: Stanley Osher
published in: Journal of Computational Physics
publication date: 1996-07-02T00:00:00Z
review text: The paper is commited to constructing high-order accurate numerical methods for solving nonlinear partial differential equations whose solutions (or their derivatives) develop steep gradients, here for the special case of the so-called nonlinear scalar Hamilton-Jacobi equations (of first order). A polynomial finite element technique, based on the ``essentially nonoscillatory schemes'' of the second author and \textit{J. A. Sethian} [J. Comput. Phys. 79, No. 1, 12-49 (1988; Zbl 0659.65132)], is used in an arbitrary domain, even with complicated boundaries (discretized in a conventional manner), combined with high-order Runge-Kutta schemes for the time steps. Numerical experiments are made for an optimal control problem, for a combustion problem, and for a problem due to P. L. Lions: a shape reconstruction from a shading problem, see also \textit{E. Rouy} and \textit{A. Tourin} [SIAM J. Number. Anal. 29, No. 3, 867-884 (1992; Zbl 0754.65069)].
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 70H20
Mathematics Subject Classification ID: 35L60
zbMATH DE Number: 881851
zbMATH Keywords: essentially nonoscillatory schemes
zbMATH Keywords: numerical experiments
zbMATH Keywords: nonlinear scalar Hamilton-Jacobi equations
zbMATH Keywords: finite element
zbMATH Keywords: Runge-Kutta schemes
zbMATH Keywords: optimal control problem
zbMATH Keywords: combustion problem
reviewed by: E. Lanckau
MaRDI profile type: Publication
full work available at URL: jcph.1996.0021
OpenAlex ID: W1984072415
DOI: 10.1006/JCPH.1996.0021
description: scientific article; zbMATH DE number 881851