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Hermite interpolation of nonsmooth functions preserving boundary conditions


Authors: V. Girault and L. R. Scott
Journal: Math. Comp. 71 (2002), 1043-1074
MSC (2000): Primary 65D05; Secondary 65N15, 65N30
DOI: https://doi.org/10.1090/S0025-5718-02-01446-1
Published electronically: January 17, 2002
MathSciNet review: 1898745
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Abstract: This article is devoted to the construction of a Hermite-type regularization operator transforming functions that are not necessarily ${\mathcal C}^1$ into globally ${\mathcal C}^1$ finite-element functions that are piecewise polynomials. This regularization operator is a projection, it preserves appropriate first and second order polynomial traces, and it has approximation properties of optimal order. As an illustration, it is used to discretize a nonhomogeneous Navier-Stokes problem, with tangential boundary condition.


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Additional Information

V. Girault
Affiliation: Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, 75252 Paris cedex 05, France
Email: girault@ann.jussieu.fr

L. R. Scott
Affiliation: Department of Mathematics and the Computation Institute, University of Chicago, Chicago, Illinois 60637-1581
Email: ridg@uchicago.edu

DOI: https://doi.org/10.1090/S0025-5718-02-01446-1
Keywords: Hermite interpolation, regularization, divergence-zero finite elements, Leray-Hopf lifting
Received by editor(s): October 15, 1999
Published electronically: January 17, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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