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Article
Polynomial Extension Operators. Part I
Mathematics and Statistics Faculty Publications and Presentations
  • Leszek Demkowicz, University of Texas at Austin
  • Jay Gopalakrishnan, Portland State University
  • Joachim Schöberl, Institute for Analysis and Scientific Computing
Document Type
Post-Print
Publication Date
1-1-2008
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 H½(∂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 Information
Leszek Demkowicz, Jay Gopalakrishnan and Joachim Schöberl. "Polynomial Extension Operators. Part I" (2008)
Available at: http://works.bepress.com/jay-gopalakrishnan/94/