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Calcolo

, Volume 49, Issue 1, pp 63–71 | Cite as

W1,q stability of the Fortin operator for the MAC scheme

  • T. Gallouët
  • R. HerbinEmail author
  • J.-C. Latché
Article

Abstract

We prove in this paper the continuity of the natural projection operator from \(W^{1,q}_{0}(\varOmega )^{d}\), q∈[1,+∞), d=2 or d=3, to the MAC discrete space of piecewise constant functions over the dual cells, endowed with the finite volume \(W_{0}^{1,q}\)-discrete norm. Since this projection operator is also a Fortin operator (that is an operator which “preserves” the divergence), this result may be applied to control the pressure in mixed problems where the test function for the velocity must be more regular than \(H^{1}_{0}(\varOmega )^{d}\).

Keywords

MAC scheme Projection stability Fortin operator 

Mathematics Subject Classification (2000)

65M12 76D07 76M12 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Université de ProvenceMarseille cedexFrance
  2. 2.Institut de Radioprotection et Sûreté Nucléaire (IRSN)St Paul-lez-Durance cedexFrance

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