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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

   

 

The lifting of polynomial traces revisited


Authors: Christine Bernardi, Monique Dauge and Yvon Maday
Journal: Math. Comp. 79 (2010), 47-69
MSC (2000): Primary 26D05, 42C05, 65N35, 46G15
Published electronically: July 24, 2009
MathSciNet review: 2552217
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct a lifting operator of polynomial traces on an interval that is stable in appropriate Sobolev norms. Next we extend this result to the case of traces vanishing at the endpoints of the interval. This has two applications, the interpolation of polynomial spaces and the evaluation by discrete formulas of fractional order Sobolev norms on polynomials.


Résumé
Nous construisons un opérateur de relèvement de traces polynômiales sur un intervalle qui est stable par rapport à des normes de Sobolev appropriées. Puis nous étendons ce résultat au cas de traces nulles aux extrémités de l'intervalle. Ceci a deux applications: l'interpolation d'espaces de polynômes, l'évaluation par des formules discrètes de normes de Sobolev d'ordre non entier appliquées à des polynômes.


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Additional Information

Christine Bernardi
Affiliation: Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, Boîte courrier 187, 4 place Jussieu, 75252 Paris Cedex 05, France
Email: bernardi@ann.jussieu.fr

Monique Dauge
Affiliation: IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France
Email: monique.dauge@univ-rennes1.fr

Yvon Maday
Affiliation: UPMC University Paris 06, UMR7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
Email: maday@ann.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-09-02259-5
Received by editor(s): January 29, 2008
Received by editor(s) in revised form: October 11, 2008
Published electronically: July 24, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.