Algebraic functions, Polynomials, Sobolev spaces, Finite element method, Mathematics -- Philosophy
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.
Demkowicz, Leszek; Gopalakrishnan, Jay; and Schöberl, Joachim, "Polynomial Extension Operators. Part I" (2008). Mathematics and Statistics Faculty Publications and Presentations. 61.