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A classical technique to construct polynomial preserving extensions of scalarfunctions defined on the boundary of an $n$ simplex to the interior is to useso-called rational blending functions. The purpose of this paper is togeneralize the construction by blending to the de Rham complex. More precisely,we define polynomial preserving extensions which map traces of $k$ formsdefined on the boundary of the simplex to $k$ forms defined in the interior.Furthermore, the extensions are cochain maps, i.e., they commute with theexterior derivative.

Construction of polynomial preserving cochain extensions by blending