“Geometrical degrees of freedom for Whitney elements”
Mercoledì 27 Aprile 2022, ore 12:30 - Sala Riunioni 702 e Zoom - Ludovico Bruni Bruno (Università di Trento)
Abstract
We consider weights as degrees of freedom for high order Whitney finite elements. They are integrals of Whitney $k$-forms over $k$-simplices. Their unisolvence is numerically proven by verifying that the associated generalised Vandermonde matrix is invertible. They carry natural generalisations of several features of nodal interpolation and offer a great flexibility on the supports.
We present results stating the non-optimality of the weights supported on $k$-simplices with vertices located at uniformly distributed points and we propose a technique to define $k$-simplices with vertices at well-known non-uniform distributions of nodes that are optimal for multivariate interpolation and computable by an explicit algorithm. Numerical results for $k > 0$ in $\mathbb{R}^2$ and $\mathbb{R}^3$ are presented and motivate this choice.
