High Order Essentially Non-Oscillatory Schemes for Hamilton-Jacobi Equations

Abstract

Hamilton-Jacobi (H-J) equations are frequently encountered in applications, e.g. in control theory and differential games. H-J equations are closely related to hyperbolic conservation laws -- in one space dimension the former is simply the integrated version of the latter. Similarity also exists for the multi-dimensional case, and this is helpful in the design of difference approximations. In this paper we investigate high order essentially non- oscillatory (ENO) schemes for H-J equations, which yield uniform high order accuracy in smooth regions and resolve discontinuities in the derivatives sharply. The ENO scheme construction procedure is adapted from that for hyperbolic conservation laws. We numerically test the schemes on a variety of one-dimensional and two-dimensional problems, including a problem related to control optimization, and observe high order accuracy in smooth regions, good resolution of discontinuities in the derivatives, and convergence to viscosity solutions. (edc)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1990
Accession Number
ADA219518

Entities

People

  • Chi-Wang Shu
  • Stanley Osher

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Aeronautics
  • Algorithms
  • Applied Mathematics
  • Cauchy Problem
  • Computers
  • Construction
  • Control Theory
  • Convergence
  • Discontinuities
  • Engineering
  • Equations
  • Errors
  • Mathematics
  • Numerical Analysis
  • Two Dimensional
  • Viscosity

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space