Some nonconforming mixed box schemes for elliptic problems

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 P1 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