, Volume 43, Issue 4, pp 287–306 | Cite as

A discrete de Rham complex with enhanced smoothness

  • Xue–Cheng Tai
  • Ragnar Winther
Open Access


Discrete de Rham complexes are fundamental tools in the construction of stable elements for some finite element methods. The purpose of this paper is to discuss a new discrete de Rham complex in three space dimensions, where the finite element spaces have extra smoothness compared to the standard requirements. The motivation for this construction is to produce discretizations which have uniform stability properties for certain families of singular perturbation problem. In particular, we show how the spaces constructed here lead to discretizations of Stokes type systems which have uniform convergence properties as the Stokes flow approaches a Darcy flow.

Keywords: Discrete exact sequences, nonconforming finite elements, Darcy–Stokes flow, uniform error estimates.

Mathematics Subject Classification (1991): Primary 65N12, 65N15, 65N30


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Xue–Cheng Tai
    • 1
  • Ragnar Winther
    • 2
  1. 1.Department of Mathematics, University of Bergen, 5007 BergenNorway
  2. 2.Centre of Mathematics for Applications and Department of Informatics, University of Oslo, 0316 OsloNorway

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