Volume 56, Number 6, November-December 2022
|Page(s)||2239 - 2253|
|Published online||08 December 2022|
Unisolvent and minimal physical degrees of freedom for the second family of polynomial differential forms
Dipartimento di Matematica, Université di Trento, Via Sommarive 14, 38123 Povo, Italy
* Corresponding author: firstname.lastname@example.org
Accepted: 23 October 2022
The principal aim of this work is to provide a family of unisolvent and minimal physical degrees of freedom, called weights, for Nédélec second family of finite elements. Such elements are thought of as differential forms PrΛk(T) whose coefficients are polynomials of degree r. In this paper we confine ourselves in the two dimensional case ℝ2, as in this framework the Five Lemma offers a neat and elegant treatment avoiding computations on the middle space. The majority of definitions and constructions are meaningful for n > 2 as well and, when possible, they are thus given in such a generality, although more complicated techniques shall be invoked to replace the graceful role of the Five Lemma. In particular, we use techniques of homological algebra to obtain degrees of freedom for the whole diagram
being T a 2-simplex of ℝ2. This work pairs its companions recently appeared for Nédélec first family of finite elements.
Mathematics Subject Classification: 65D05 / 65D99 / 53A70
Key words: High order elements / Whitney forms / Nédélec second family / weights / physical degrees of freedom
© The authors. Published by EDP Sciences, SMAI 2022
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