The lifting of polynomial traces revisited

Bernardi, Christine; Dauge, Monique; Maday, Yvon

doi:10.1090/S0025-5718-09-02259-5

The lifting of polynomial traces revisited
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by Christine Bernardi, Monique Dauge and Yvon Maday PDF

Math. Comp. 79 (2010), 47-69 Request permission

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. \center Résumé \endcenter 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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