A Note on the Accuracy of Spectral Method Applied to Nonlinear Conservation Laws

Abstract

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials. Spectral method, Accuracy, Gibbs phenomenon, Nonlinear conservation laws.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1994
Accession Number
ADA284063

Entities

People

  • Chi-Wang Shu
  • Peter S. Wong

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Analytic Functions
  • Applied Mathematics
  • Case Studies
  • Coefficients
  • Contracts
  • Differential Equations
  • Discontinuities
  • Engineering
  • Equations
  • Frequency
  • Galerkin Method
  • Mathematics
  • Partial Differential Equations
  • Periodic Functions
  • Polynomials

Readers

  • Calculus or Mathematical Analysis
  • Computational Modeling and Simulation