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A note on polynomial approximation in Sobolev spaces

Published online by Cambridge University Press:  15 August 2002

Rüdiger Verfürth
Rüdiger Verfürth*
Affiliation:
Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany. rv@silly.num1.ruhr-uni-bochum.de.
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Abstract

For domains which are star-shapedw.r.t. at least one point, we give new bounds on theconstants in Jackson-inequalities in Sobolev spaces. Forconvex domains, these bounds do not depend on theeccentricity. For non-convex domains with a re-entrantcorner, the bounds are uniform w.r.t. the exteriorangle. The main tool is a new projection operator ontothe space of polynomials.

Keywords

Jackson inequalitiespolynomial approximationSobolev spaces.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 4 , July 1999 , pp. 715 - 719
Copyright
© EDP Sciences, SMAI, 1999

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