Analysis of the Scott-Zhang interpolation in the fractional order Sobolev spaces

Patrick Ciarlet 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : Since it was originally designed, the Scott-Zhang interpolation operator has been very popular. Indeed, it possesses two keys features: it can be applied to fields without pointwise values and it preserves the boundary condition. However, no approximability properties seem to be available in the literature when the regularity of the field is weak. In this Note, we provide some estimates for such weakly regular fields, measured in Sobolev spaces with fractional order between 0 and 1
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https://hal.inria.fr/hal-00937677
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Submitted on : Tuesday, January 28, 2014 - 5:06:09 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:03 AM

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Patrick Ciarlet. Analysis of the Scott-Zhang interpolation in the fractional order Sobolev spaces. Journal of Numerical Mathematics, De Gruyter, 2013, 21 (3), pp.173-180. ⟨10.1515/jnum-2013-0007⟩. ⟨hal-00937677⟩

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