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