Polynomial extension operators. Part III

Authors:
L. Demkowicz, J. Gopalakrishnan and J. Schöberl

Journal:
Math. Comp. **81** (2012), 1289-1326

MSC (2010):
Primary 46E35, 46E40; Secondary 41A10, 65D05, 65L60

DOI:
https://doi.org/10.1090/S0025-5718-2011-02536-6

Published electronically:
September 20, 2011

MathSciNet review:
2904580

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this concluding part of a series of papers on tetrahedral polynomial extension operators, the existence of a polynomial extension operator in the Sobolev space is proven constructively. Specifically, on any tetrahedron , given a function on the boundary that is a polynomial on each face, the extension operator applied to gives a vector function whose components are polynomials of at most the same degree in the tetrahedron. The vector function is an extension in the sense that the trace of its normal component on the boundary coincides with . Furthermore, the extension operator is continuous from into . The main application of this result and the results of this series of papers is the existence of commuting projectors with good -approximation properties.

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Additional Information

**L. Demkowicz**

Affiliation:
Institute of Computational Engineering and Sciences, 1 University Station, C0200, The University of Texas at Austin, Texas 78712

Email:
leszek@ices.utexas.edu

**J. Gopalakrishnan**

Affiliation:
University of Florida, Department of Mathematics, Gainesville, Florida 32611–8105

Email:
jayg@ufl.edu

**J. Schöberl**

Affiliation:
Technische Universität Wein, Wiedner Hauptstrasse 8-10, Wein 1040, Austria

Email:
joachim.schoeberl@tuwien.ac.at

DOI:
https://doi.org/10.1090/S0025-5718-2011-02536-6

Received by editor(s):
January 3, 2010

Received by editor(s) in revised form:
February 23, 2011

Published electronically:
September 20, 2011

Additional Notes:
This work was supported in part by the National Science Foundation under grants DMS-1014817, the Johann Radon Institute for Computational and Applied Mathematics (RICAM), and the FWF-Start-Project Y-192 “hp-FEM”

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.