Sponsor
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".
Published In
Mathematics of Computation
Document Type
Post-Print
Publication Date
2011
Subjects
Approximation theory, Mathematical analysis, Functional analysis, Polynomials
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 H(div) is proven constructively. Specifically, on any tetrahedron K, given a function w on the boundary ∂K that is a polynomial on each face, the extension operator applied to w 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 ∂K coincides with w. Furthermore, the extension operator is continuous from H-½(∂K) into H(div,K). The main application of this result and the results of this series of papers is the existence of commuting projectors with good hp-approximation properties.
Rights
Mathematics of Computation © 2012 American Mathematical Society
Locate the Document
DOI
10.1090/S0025-5718-2011-02536-6
Persistent Identifier
http://archives.pdx.edu/ds/psu/10612
Citation Details
Published as: DEMKOWICZ, L., GOPALAKRISHNAN, J., & SCHÖBERL, J. (2012). POLYNOMIAL EXTENSION OPERATORS. PART III. Mathematics of Computation, 81(279), 1289–1326.
Description
This is an Author's Original Manuscript of an article that was first published in Mathematics of Computation in December 2011, Vol. 81 Issue 279, p1289-1326. Published by the American Mathematical Society.