On high order finite element spaces of differential forms

2013/06/20 by Snorre H. Christiansen, Christiansen, Snorre Harald, Francesca Rapetti +1 · 3 citations
Engineering · #58A10 #65N30 #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · doi:10.48550/arxiv.1306.4835

openalex publication_date 2013/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Interpretation of a Discrete de Rham method as a Finite Element System
• Conforming lifting and adjoint consistency for the Discrete de Rham complex of differential forms
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