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Some nonconforming mixed box schemes for elliptic problems
Author(s) -
Croisille JeanPierre,
Greff Isabelle
Publication year - 2002
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10003
Subject(s) - mathematics , scheme (mathematics) , polygon mesh , quadratic equation , space (punctuation) , discontinuous galerkin method , representation (politics) , partial differential equation , pure mathematics , mathematical analysis , finite element method , geometry , computer science , physics , politics , political science , law , thermodynamics , operating system
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