Monotone Difference Approximations for Scalar Conservation Laws.

Abstract

A complete self-contained treatment of the stability and convergence properties of conservation form, monotone difference approximations to scalar conservation laws in several space variables is developed. In particular, the authors prove that general monotone difference schemes always converge and that they converge to the physical weak solution satisfying the entropy condition. Rigorous convergence results follow for dimensional splitting algorithms when each step is approximated by a monotone difference scheme. The results are general enough to include, for instance, Godunov's scheme, the upwind scheme (Differenced through stagnation points), and the Lax-Friedrichs scheme together with appropriate multi-dimensional generalizations. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1979
Accession Number
ADA068905

Entities

People

  • Andrew Majda
  • Michael G. Crandall

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Complex Variables
  • Continuum Mechanics
  • Contracts
  • Convergence
  • Differential Equations
  • Equations
  • Fluid Flow
  • Geometry
  • Mathematical Analysis
  • Mathematics
  • Military Research
  • North Carolina
  • Numerical Analysis
  • Partial Differential Equations
  • Stagnation Point
  • United States

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space