An invariant moving mesh scheme for the nonlinear diffusion equation
type: Item
instance of: scholarly article
title: An invariant moving mesh scheme for the nonlinear diffusion equation
zbMATH Open document ID: 0911.65081
DOI: 10.1016/S0168-9274(97)00079-2
author: G. J. Collins
author: C. J. Budd
published in: Applied Numerical Mathematics
publication date: 1999-04-26T00:00:00Z
review text: The main purpose of the paper is to present some theoretical and numerical aspects of the Cauchy problem for the nonlinear diffusion equation \(u_t= (u^mu_x)_x\), \(m\in\mathbb{R}\), \(m>-2\), which is posed on an infinite domain. When solving such problems one can use the information given by the invariance of this problem to a Lie group of stretchings. The problem is semi-discretized using the method of lines and the discrete solutions are desired to have the same asymptotic behaviour as solutions of the continuous problem. Hence the main role plays the fact that the derived scheme has the same conserved quantities and the same invariants as the continuous problem. (Shortened review; the full text is available at Zbl).
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1115977
zbMATH Keywords: moving mesh
zbMATH Keywords: invariant mesh
zbMATH Keywords: Cauchy problem
zbMATH Keywords: nonlinear diffusion equation
zbMATH Keywords: Lie group
zbMATH Keywords: method of lines
reviewed by: S. Burys
describes a project that uses: DASSL
MaRDI profile type: Publication
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Wikidata QID: Q127633872
full work available at URL: s0168-9274(97)00079-2
OpenAlex ID: W1988083967
description: scientific article; zbMATH DE number 1115977