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On high order finite element spaces of differential forms


Authors: Snorre H. Christiansen and Francesca Rapetti
Journal: Math. Comp. 85 (2016), 517-548
MSC (2010): Primary 65N30, 58A10
Published electronically: July 10, 2015
MathSciNet review: 3434870
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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.


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Additional Information

Snorre H. Christiansen
Affiliation: Department of Mathematics, University of Oslo, PO box 1053 Blindern, NO-0316 Oslo, Norway
Email: snorrec@math.uio.no

Francesca Rapetti
Affiliation: Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
Email: Francesca.RAPETTI@unice.fr

DOI: https://doi.org/10.1090/mcom/2995
Keywords: Finite elements, differential forms, high order approximations
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.
Article copyright: © Copyright 2015 American Mathematical Society