## Discrete and conforming smooth de Rham complexes in three dimensions

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- by Michael Neilan PDF
- Math. Comp.
**84**(2015), 2059-2081 Request permission

## Abstract:

Conforming discrete de Rham complexes consisting of finite element spaces with extra smoothness are constructed. In particular, we develop $H^2$, $\boldsymbol {H}^1({\text {curl}})$, $\boldsymbol {H}^1$ and $L^2$ conforming finite element spaces and show that an exactness property is satisfied. These results naturally lead to discretizations for Stokes and Brinkman type problems as well as conforming approximations to fourth order curl problems. In addition, we reduce the question of stability of the three-dimensional Scott-Vogelius finite element to a simply stated conjecture.## References

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## Additional Information

**Michael Neilan**- Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- MR Author ID: 824091
- Email: neilan@pitt.edu
- Received by editor(s): May 30, 2013
- Received by editor(s) in revised form: January 3, 2014
- Published electronically: March 11, 2015
- Additional Notes: This work was supported in part by the National Science Foundation through grant number DMS-1115421.
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp.
**84**(2015), 2059-2081 - MSC (2010): Primary 65N30, 65N12, 76M10
- DOI: https://doi.org/10.1090/S0025-5718-2015-02958-5
- MathSciNet review: 3356019