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 the exactness, we show that the usual three-dimensional sequence of trimmed Finite Element (FE) spaces forms, through appropriate interpolation operators, a commutative diagram with our sequence, which ensures suitable approximation properties. A discussion on reconstructions of potentials and discrete L2-products completes the exposition.
|Number of pages||47|
|Journal||Mathematical Models and Methods in Applied Sciences|
|Publication status||Published - 26 Aug 2020|
- compatible discretisations
- Fully discrete de Rham sequences
- mixed methods
- polyhedral methods