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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board Member: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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Volume 21, Issue 3 (Oct 2013)


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

Patrick Ciarlet
  • Corresponding author
  • POEMS Laboratory UMR CNRS-ENSTA-INRIA 7231, ENSTA ParisTech, 828, boulevard des Mar´echaux 91762 Palaiseau Cedex, France
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Published Online: 2013-10-16 | DOI: https://doi.org/10.1515/jnum-2013-0007


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.

Keywords : finite elements; approximation properties; Scott-Zhang interpolation

About the article

Published Online: 2013-10-16

Published in Print: 2013-10-01

Citation Information: Journal of Numerical Mathematics, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnum-2013-0007.

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