Difference schemes on uniform grids performed by general discrete operators
type: Item
instance of: scholarly article
title: Difference schemes on uniform grids performed by general discrete operators
zbMATH Open document ID: 1057.65070
author: Enrique Bendito
author: A. Carmona
author: A. M. Encinas
published in: Applied Numerical Mathematics
publication date: 2004-08-19T00:00:00Z
review text: The paper is devoted to rather formal constructions of grid approximations on uniform grids for \(n\)-dimensional linear elliptic equations. As a key tool, difference analogues of gradient and divergence operators are used. The first and second order approximations are considered. Under the difference scheme, ``an expression of the form \(L_h(u)(x)\)'' (a difference formula) is understood which is defined mainly for finite functions on the uniform grid in \(\mathbb R^n\). Reviewer's remarks: Grid analogues of gradient and divergence operators and their applications were considered in many papers [for example, \textit{V. I. Lebedev}, Zh. Vychisl. Mat. Mat. Fiz. 4, 449--465, 649--659 (1964; Zbl 0158.34301)], but for the case of more involved boundary conditions it is known that grid analogues of the basic integral identity are more helpful. Some notions in the paper are not properly defined; for example, on page 345 the definition of ``\(r\)-consistent scheme'' makes use of \(O(h^r)\) estimate for a grid function without specification of its sense (it is well known that the choice of the norm is very important).
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N50
zbMATH DE Number: 2093395
zbMATH Keywords: elliptic equations
zbMATH Keywords: difference approximations
zbMATH Keywords: uniform grids
zbMATH Keywords: discrete vector calculus
zbMATH Keywords: mimetic finite difference methods
zbMATH Keywords: discrete metric tensors
reviewed by: Evgeniĭ Dyakonov
MaRDI profile type: Publication
full work available at URL: j.apnum.2004.01.010
OpenAlex ID: W2091707269
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DOI: 10.1016/J.APNUM.2004.01.010
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description: scientific article; zbMATH DE number 2093395