Séminaire ACSIOM :

Le 08 décembre 2020 à 13.15 - salle 109 (1er étage)

Présentée par Di Pietro Daniele - IMAG, Montpellier

Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra

En commun avec l'exposé NAGANA

In this work, merging ideas from compatible discretisations and polyhedral methods, we construct novel fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra. The spaces and operators that appear in these sequences are directly amenable to computer implementation. Besides proving exactness, we show that the usual three-dimensional sequence of trimmed Finite Element spaces forms, through appropriate interpolation operators, a commutative diagram with our sequence, which ensures suitable approximation properties. The discrete de Rham (DDR) sequence is then used to design a stable arbitrary-order approximation of a magnetostatics problem.