Construction of polynomial preserving cochain extensions by blending

Falk, Richard; Winther, Ragnar

doi:10.1090/mcom/3819

Construction of polynomial preserving cochain extensions by blending
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by Richard S. Falk and Ragnar Winther HTML | PDF

Math. Comp. 92 (2023), 1575-1594 Request permission

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.

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