Some nonconforming mixed box schemes for elliptic problems

✍ Scribed by Jean-Pierre Croisille; Isabelle Greff

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 181 KB
• Volume: 18
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.10003

✦ Synopsis

Abstract

In this article, we introduce three schemes for the Poisson problem in 2D on triangular meshes, generalizing the FVbox scheme introduced by Courbet and Croisille [1]. In this kind of scheme, the approximation is performed on the mixed form of the problem, but contrary to the standard mixed method, with a pair of trial spaces different from the pair of test spaces. The latter is made of Galerkin‐discontinuous spaces on a unique mesh. The first scheme uses as trial spaces the P^1^ nonconforming space of Crouzeix‐Raviart both for u and for the flux p = ∇u. In the two others, the quadratic nonconforming space of Fortin and Soulie is used. An important feature of all these schemes is that they are equivalent to a first scheme in u only and an explicit representation formula for the flux p = ∇u. The numerical analysis of the schemes is performed using this property. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 355–373, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10003