Quadratic convergence for cell-centered grids
type: Item
instance of: scholarly article
title: Quadratic convergence for cell-centered grids
zbMATH Open document ID: 0651.65086
DOI: 10.1016/0168-9274(88)90016-5
author: P. H. Sammon
author: P. A. Forsyth
published in: Applied Numerical Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Rectangular cell-centered finite difference approximations of a plane pressure-flow equation in a rectangular region with no-flow conditions at the boundary are considered. Despite a formal inconsistency in the finite difference equations, due to the use of cell-centered rather than point- distributed grids, it is shown that the solution errors are \(O(h^ 2)\) when the mesh width \(h\to 0\). The methods are quite elementary and rely upon an explicit treatment of truncation error terms which are not \(O(h^ 2)\).
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 4062527
zbMATH Keywords: Taylor series expansion
zbMATH Keywords: order of convergence
zbMATH Keywords: cell-centered grids
zbMATH Keywords: finite difference approximations
zbMATH Keywords: plane pressure-flow equation
zbMATH Keywords: formal inconsistency
zbMATH Keywords: truncation error
reviewed by: S. Leif Svensson
MaRDI profile type: Publication
full work available at URL: 0168-9274(88)90016-5
OpenAlex ID: W2007628212
cites work: Volume of fluid (VOF) method for the dynamics of free boundaries
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cites work: The Numerical Solution of Second-Order Boundary Value Problems on Nonuniform Meshes
cites work: On Convergence of Block-Centered Finite Differences for Elliptic Problems
description: scientific article; zbMATH DE number 4062527