Supraconvergence of a class of moving grid methods for solving a nonlinear problem
type: Item
instance of: scholarly article
title: Supraconvergence of a class of moving grid methods for solving a nonlinear problem
zbMATH Open document ID: 0859.65093
DOI: 10.1016/0168-9274(95)00135-2
published in: Applied Numerical Mathematics
publication date: 1997-04-07T00:00:00Z
review text: The author proves a so-called supraconvergence result for finite difference schemes on nonuniform spatial grids discretizing quasilinear parabolic equations. By supraconvergence one denotes the phenomenon that the approximate solutions are second-order in the spatial grid size convergent although the scheme has a first-order truncation error only. The grid is assumed to vary not too strongly with respect to time which is the case if familiar monitoring criteria for the grid distribution are used. The proof of the result is based on an a priori estimate for nonlinear boundary value problems of ordinary differential equations which generalizes Spijker-norm stability inequalities obtained by the author for linear equations.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M50
zbMATH DE Number: 897559
zbMATH Keywords: moving grid methods
zbMATH Keywords: method of lines
zbMATH Keywords: supraconvergence
zbMATH Keywords: finite difference schemes
zbMATH Keywords: quasilinear parabolic equations
zbMATH Keywords: Spijker-norm stability inequalities
author: J. A. Ferreira
reviewed by: Rolf Dieter Grigorieff
MaRDI profile type: Publication
full work available at URL: 0168-9274(95)00135-2
OpenAlex ID: W2019374462
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description: scientific article; zbMATH DE number 897559