Incremental unknowns in finite differences in three space dimensions
type: Item
instance of: scholarly article
title: Incremental unknowns in finite differences in three space dimensions
zbMATH Open document ID: 0841.65089
author: Min Chen
author: R. Temam
author: Alain Miranville
published in: Computational and Applied Mathematics
publication date: 1996-07-25T00:00:00Z
review text: The incremental unknowns have been applied to numerous problems, see the introduction of the present paper. The aim of this paper is to study the Laplace equation on the cube \((0,1)^3\). The second-order incremental unknowns are introduced and studied. By deriving suitable prior estimates it is proved that incremental unknowns are small. Then, the condition number of the matrix corresponding to the five-point discretization of the Laplace equation is analyzed. The authors show that this number is \(O(h^{-1} \ln(h)^4)\) instead of \(O(h^{-2})\) when the usual nodal unknowns are used, with \(h\) being the fine grid mesh size.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 854781
zbMATH Keywords: finite differences
zbMATH Keywords: incremental unknowns
zbMATH Keywords: Laplace equation
zbMATH Keywords: condition number
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 854781