Uniformly High-Order Accurate Non-Oscillatory Schemes I.

Abstract

The authors begin the construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first order accuracy, in the sense of truncation error, at extrema of the solution. This paper constructs a uniformly second order approximation, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution form its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. Additional Keywords: Computations; Charts; operators(mathematics). (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1985
Accession Number
ADA158177

Entities

People

  • A. Harten
  • S. Osher

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Cauchy Problem
  • Consortiums
  • Construction
  • Contracts
  • Differential Equations
  • Equations
  • Errors
  • Euler Equations
  • High Resolution
  • Mathematics
  • North Carolina
  • Numerical Analysis
  • Truncation
  • United States
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

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