Title: Construction of polynomial preserving cochain extensions
by blending
Authors: Richard S. Falk and Ragnar Winther
Source: Math. Comp. (92), No. 342, 2023, 1575--1594
Abstract:
A classical technique to construct polynomial preserving extensions
of scalar functions defined on the boundary of an $n$ simplex to the
interior is to use so-called rational blending functions. The
purpose of this paper is to generalize the construction by blending
to the de Rham complex. More precisely, we define polynomial
preserving extensions which map traces of $k$ forms
defined on the boundary of the simplex to $k$ forms defined in the interior.
Furthermore, the extensions are cochain maps, i.e., they commute
with the exterior derivative.
Key words: blending methods, simplices, differential forms, cochain extensions,
preservation of polynomial spaces
AMS(MOS) subject classifications. Primary: 65N30, 65D17, 65D18