Polynomial Extension Operators. Part I

Authors

Leszek Demkowicz, University of Texas at AustinFollow
Jay Gopalakrishnan, Portland State UniversityFollow
Joachim Schöberl, Institute for Analysis and Scientific ComputingFollow

Document Type

Post-Print

Publication Date

2008

Subjects

Algebraic functions, Polynomials, Sobolev spaces, Finite element method, Mathematics -- Philosophy

Abstract

In this series of papers, we construct operators that extend certain given functions on the boundary of a tetrahedron into the interior of the tetrahedron, with continuity properties in appropriate Sobolev norms. These extensions are novel in that they have certain polynomial preservation properties important in the analysis of high order finite elements. This part of the series is devoted to introducing our new technique for constructing the extensions, and its application to the case of polynomial extensions from H^½(∂K) into H¹(K), for any tetrahedron K.

Description

This is the author’s version of a work that was accepted for publication in SIAM Journal on Numerical Analysis. A definitive version was subsequently published in SIAM Journal on Numerical Analysis, 2008. Vol. 46 Issue 6, p. 3006-3031.

DOI

10.1137/070698786

Persistent Identifier

http://archives.pdx.edu/ds/psu/10705

Citation Details

Demkowicz, Leszek; Gopalakrishnan, Jay; and Schöberl, Joachim, "Polynomial Extension Operators. Part I" (2008). Mathematics and Statistics Faculty Publications and Presentations. 61.
http://archives.pdx.edu/ds/psu/10705