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- W2811216522 abstract "In order to generalize finite element methods to differential forms, Arnold, Falk, and Winther constructed two families of spaces of polynomial differential forms on a simplex $T$, the $mathcal P_rLambda^k(T)$ spaces and the $mathcal P_r^-Lambda^k(T)$ spaces, where $k$ is the degree of the form and $r$ is the degree of its coefficients. The geometric decomposition for these finite element spaces hinges on a duality relationship between the $mathcal P$ and $mathcal P^-$ spaces proved by Arnold, Falk, and Winther. In this article, we give a natural alternate construction of the $mathcal P_rLambda^k(T)$ and $mathcal P_r^-Lambda^k(T)$ spaces, leading to a new basis-free proof of this duality relationship using a modified Hodge star operator." @default.
- W2811216522 created "2018-07-10" @default.
- W2811216522 creator A5089033864 @default.
- W2811216522 date "2018-06-30" @default.
- W2811216522 modified "2023-09-27" @default.
- W2811216522 title "Duality in finite element exterior calculus" @default.
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- W2811216522 hasPublicationYear "2018" @default.
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