This work was supported in part by the National Science Foundation under grants 0713833, 0619080, the Johann Radon Institute for Computational and Applied Mathematics (RICAM), and the FWF-Start-Project Y-192 “hp-FEM”
Finite element method, Polynomials, Vector analysis, Numerical analysis
Consider the tangential trace of a vector polynomial on the surface of a tetrahedron. We construct an extension operator that extends such a trace function into a polynomial on the tetrahedron. This operator can be continuously extended to the trace space of H(curl ). Furthermore, it satisfies a commutativity property with an extension operator we constructed in Part I of this series. Such extensions are a fundamental ingredient of high order finite element analysis.
Demkowicz, Leszek; Gopalakrishnan, Jay; and Schöberl, Joachim, "Polynomial Extension Operators. Part II" (2009). Mathematics and Statistics Faculty Publications and Presentations. 57.