Geometrical degrees of freedom for Whitney elements

“Doc in Progress” and #iorestoacasa are pleased to introduce you to:

• Ludovico Bruni Bruno - University of Trento - PhD in Mathematics

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 R 2 and R 3 are presented and motivate this choice.

The seminar will be held both in presence in Seminar Room "-1" (Povo 0) and online via Zoom.

To join the event, please contact docinprogress.unitn@gmail.com using an institutional e-mail address for both reserving a sit in the seminar room or obtaining login credentials.