Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

Request Permissions   Purchase Content 
 

 

Discrete and conforming smooth de Rham complexes in three dimensions


Author: Michael Neilan
Journal: Math. Comp. 84 (2015), 2059-2081
MSC (2010): Primary 65N30, 65N12, 76M10
DOI: https://doi.org/10.1090/S0025-5718-2015-02958-5
Published electronically: March 11, 2015
MathSciNet review: 3356019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65N30, 65N12, 76M10

Retrieve articles in all journals with MSC (2010): 65N30, 65N12, 76M10


Additional Information

Michael Neilan
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: neilan@pitt.edu

DOI: https://doi.org/10.1090/S0025-5718-2015-02958-5
Keywords: Finite elements, de Rham complex, divergence free
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.
Article copyright: © Copyright 2015 American Mathematical Society