Interpolation finite difference schemes on grids locally refined in time
type: Item
instance of: scholarly article
title: Interpolation finite difference schemes on grids locally refined in time
zbMATH Open document ID: 0978.65078
DOI: 10.1016/S0045-7825(99)00451-X
author: G. I. Shishkin
author: P. N. Vabishchevich
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2002-01-21T00:00:00Z
review text: The authors consider a class of finite difference schemes with local grid refinement in time in a part of the domain and analyze their accuracy with the simplest interpolated interface conditions on the boundary of the adaptation domain. On the basis of the maximum principle, it is shown that these schemes converge uniformly in the uniform norm and the rate of convergence is analyzed. Four difference schemes are used to solve numerically a model Dirichlet problem for a second-order parabolic equation on a rectangle, namely, (a) purely implicit scheme using the basic grid, (b) scheme on a finer grid, (c) scheme with local refinement of the time grid within the adaptation domain, and (d) predictor-corrector scheme on the grid with local refinement. It is found that using a refined grid in time produces numerical solutions without loss of accuracy and with considerably smaller computational effort.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1563787
zbMATH Keywords: finite difference schemes
zbMATH Keywords: local grid refinement
zbMATH Keywords: initial boundary value problem
zbMATH Keywords: parabolic equation
zbMATH Keywords: convergence
zbMATH Keywords: Dirichlet problem
Wikidata QID: Q57694669
MaRDI profile type: Publication
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full work available at URL: s0045-7825(99)00451-x
OpenAlex ID: W2074579193
description: scientific article; zbMATH DE number 1563787