A Legendre pseudospectral viscosity method
type: Item
instance of: scholarly article
title: A Legendre pseudospectral viscosity method
zbMATH Open document ID: 0863.65065
author: S. M. Ould Kaber
published in: Journal of Computational Physics
publication date: 1996-12-18T00:00:00Z
review text: The author considers the scalar conservation law: \[ \partial_t u+\partial_xf(u)=0, \qquad u(x,0)=u_0(x), \] here \(t>0\), \(x\) lies in an open interval and the flux \(f\) is a regular function. It is known that even for smooth \(u_0\) the solution can develop discontinuities, so the problem possesses in general only weak solutions. To ensure uniqueness one needs supplementary conditions. The author considers a so called entropy inequality. To overcome Gibbs type phenomena he proposes the ``Legendre spectral vanishing viscosity'' method which consists in adding a small viscosity on the high coefficients of the numerical solution. This viscosity is small enough to stabilize the computation, ensuring the convergence of the solution of a finite-dimensional variational problem towards the exact one. Test problems show the efficiency to the numerical method.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 947673
zbMATH Keywords: numerical examples
zbMATH Keywords: Legendre spectral vanishing viscosity method
zbMATH Keywords: conservation law
zbMATH Keywords: weak solutions
zbMATH Keywords: entropy inequality
zbMATH Keywords: Gibbs type phenomena
zbMATH Keywords: convergence
MaRDI profile type: Publication
OpenAlex ID: W2016093591
DOI: 10.1006/JCPH.1996.0201
description: scientific article; zbMATH DE number 947673