Unisolvent and minimal physical degrees of freedom for the second family of polynomial differential forms
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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 𝒫_r Λ^k (T) whose coefficients are polynomials of degree r. We confine ourselves in the two dimensional case ℝ^2 since it is easy to visualise and offers a neat and elegant treatment; however, we present techniques that can be extended to n > 2 with some adjustments of technical details. In particular, we use techniques of homological algebra to obtain degrees of freedom for the whole diagram 𝒫_r Λ^0 (T) →𝒫_r Λ^1 (T) →𝒫_r Λ^2 (T), being T a 2-simplex of ℝ^2. This work pairs its companions recently appeared for Nédélec first family of finite elements.
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