#### 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.

#### DOI

10.1090/S0025-5718-2011-02536-6

#### Persistent Identifier

http://archives.pdx.edu/ds/psu/10612

#### Citation Details

Demkowicz, Leszek; Gopalakrishnan, Jay; and Schöberl, Joachim, "Polynomial Extension Operators. Part III" (2011). *Mathematics and Statistics Faculty Publications and Presentations*. 44.

https://pdxscholar.library.pdx.edu/mth_fac/44

## 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.