On High-Order Accurate Interpolation for Non-Oscillatory Shock Capturing Schemes.

Abstract

This paper describes high-order accurate Godunov-type schemes for the computation of weak solutions of hyperbolic conservation laws that are essentially non-oscillatory. It is shown that the problem of designing such schemes reduces to a problem in approximation of functions, namely that of reconstructing a piecewise smooth function from its given oscillations. To solve this reconstruction problem we introduce a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy wherever the function is smooth but avoids having a Gibbs-phenomenon at discontinuities. Additional keywords: Variables; operators(mathematics). (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1985
Accession Number
ADA158131

Entities

People

  • A. Harten

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Classification
  • Computations
  • Differential Equations
  • Discontinuities
  • Interpolation
  • Mathematics
  • North Carolina
  • Numerical Analysis
  • Oscillation
  • Partial Differential Equations
  • Polynomials
  • Security
  • Smoothing (Mathematics)
  • Truncation
  • United States

Fields of Study

  • Mathematics

Readers

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