## Section: New Results

### First steps to polytopal/polyhedral meshes

Participant : Francesca Rapetti.

Merging ideas from compatible discretisations and polyhedral methods, I have worked with D. Di Pietro and J. Droniou to 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 have shown that the usual sequence of Finite Element spaces forms, through appropriate interpolation operators, a commutative diagram with other proposed sequence, which ensures suitable approximation properties. A discussion on reconstructions of potentials and discrete L2-products completes the work [14].