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Numerische Mathematik

, Volume 86, Issue 1, pp 29–48 | Cite as

On the construction of stable curvilinear $p$ version elements for mixed formulations of elasticity and Stokes flow

  • Lawrence Chilton
  • Manil Suri
Original article

Summary. The use of mixed finite element methods is well-established in the numerical approximation of the problem of nearly incompressible elasticity, and its limit, Stokes flow. The question of stability over curved elements for such methods is of particular significance in the p version, where, since the element size remains fixed, exact representation of the curved boundary by (large) elements is often used. We identify a mixed element which we show to be optimally stable in both p and h refinement over curvilinear meshes. We prove optimal p version (up to \(O(p^{\epsilon})\)) and h version (p = 2, 3) convergence for our element, and illustrate its optimality through numerical experiments.

Mathematics Subject Classification (1991):65N30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Lawrence Chilton
    • 1
  • Manil Suri
    • 2
  1. 1.Department of Mathematics and Statistics, Air Force Institute of Technology, Wright-Patterson AFB, OH 45433, USA; e-mail: lchilton@afit.af.mil US
  2. 2.Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250, USA; e-mail: suri@math.umbc.edu US

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