Analysis of the Spectral Vanishing Viscosity Method for Periodic Conservation Laws.

Abstract

We analyze the convergence of the spectral vanishing method for both the spectral and pseudospectral discretizations of the inviscid Burgers' equation. We prove that this kind of vanishing viscosity is responsible for a spectral decay of those Fourier coefficients located toward the end of the computed spectrum; consequently, the discretization error is shown to be spectrally small independent of whether the underlying solution is smooth or not. This in turn implies that the numerical solution remains uniformly bounded and convergence follows by compensated compactness arguments.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1988
Accession Number
ADA192292

Entities

People

  • Eitan Tadmor
  • Yvon Maday

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Aeronautics
  • Coefficients
  • Contracts
  • Convergence
  • Differential Equations
  • Engineering
  • Equations
  • Errors
  • Guarantees
  • Inequalities
  • Integrals
  • Mathematics
  • Navier Stokes Equations
  • Numerical Analysis
  • Polynomials
  • Standards
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)