On high order finite element spaces of differential forms
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- by Snorre H. Christiansen and Francesca Rapetti PDF
- Math. Comp. 85 (2016), 517-548 Request permission
Abstract:
We show how the high order finite element spaces of differential forms due to Raviart-Thomas-Nédelec-Hiptmair fit into the framework of finite element systems, in an elaboration of the finite element exterior calculus of Arnold-Falk-Winther. Based on observations by Bossavit, we provide new low order degrees of freedom. As an alternative to existing choices of bases, we provide canonical resolutions in terms of scalar polynomials and Whitney forms.References
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Additional Information
- Snorre H. Christiansen
- Affiliation: Department of Mathematics, University of Oslo, PO box 1053 Blindern, NO-0316 Oslo, Norway
- MR Author ID: 663397
- Email: snorrec@math.uio.no
- Francesca Rapetti
- Affiliation: Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
- MR Author ID: 602457
- Email: Francesca.RAPETTI@unice.fr
- Received by editor(s): July 1, 2013
- Received by editor(s) in revised form: June 29, 2014, and September 9, 2014
- Published electronically: July 10, 2015
- Additional Notes: The research of SHC was funded by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement nr. 278011.
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp. 85 (2016), 517-548
- MSC (2010): Primary 65N30, 58A10
- DOI: https://doi.org/10.1090/mcom/2995
- MathSciNet review: 3434870