## Construction of polynomial preserving cochain extensions by blending

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Richard S. Falk and Ragnar Winther
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## 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.## References

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## Additional Information

**Richard S. Falk**- Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
- MR Author ID: 65045
- ORCID: 0000-0002-9082-7348
- Email: falk@math.rutgers.edu
**Ragnar Winther**- Affiliation: Department of Mathematics, University of Oslo, 0316 Oslo, Norway
- MR Author ID: 183665
- Email: rwinther@math.uio.no
- Received by editor(s): February 6, 2022
- Received by editor(s) in revised form: December 5, 2022
- Published electronically: February 2, 2023
- Additional Notes: The research leading to these results received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement 339643.
- © Copyright 2023 American Mathematical Society
- Journal: Math. Comp.
**92**(2023), 1575-1594 - MSC (2020): Primary 65N30, 65D17, 65D18
- DOI: https://doi.org/10.1090/mcom/3819
- MathSciNet review: 4570334