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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
117/2005

Nonconforming box-schemes for elliptic problems on rectangular grids

Isabelle Greff

Abstract

Recently, Courbet and Croisille [Math.Model.Numer.Anal., 32, 631--649, 1998] introduced the FV box-scheme for the 2D Poisson problem in the case of triangular meshes. Generalization to higher degree box-schemes has been published by Croisille and Greff [Numer. Methods Partial Differential Equations, 18, 355--373, 2002].

These box-schemes are based on the idea of the finite volume method in that they take the average of the equations on each cell of the mesh. This gives rise to a natural choice of unknowns located at the interface of the mesh. Contrary to the finite volume method, these box-schemes are conservative and use only one mesh. They can be seen as a discrete mixed Petrov-Galerkin formulation of the Poisson problem. In this paper we focus our interest on box-schemes for the Poisson problem in 2D on rectangular grids. We discuss the basic FV box-scheme, and analyse and interpret it as three different box-schemes. The method is demonstrated by numerical examples.

Received:
Dec 10, 2005
Published:
Dec 10, 2005
MSC Codes:
35J20, 65N30, 65N12
Keywords:
box-scheme, petrov-galerkin formulation, mixed method, elliptic problems, finite volume method, finite element method

Related publications

inJournal
2007 Repository Open Access
Isabelle Greff

Nonconforming box-schemes for elliptic problems on rectangular grids

In: SIAM journal on numerical analysis, 45 (2007) 3, pp. 946-968