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Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2020

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

Résumé

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 sequence of Finite Element 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 $L^2$-products completes the exposition.
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Dates et versions

hal-02356810 , version 1 (09-11-2019)
hal-02356810 , version 2 (04-06-2021)

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Daniele Antonio Di Pietro, Jerome Droniou, Francesca Rapetti. Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra. Mathematical Models and Methods in Applied Sciences, 2020, 30 (9), pp.1809-1855. ⟨10.1142/S0218202520500372⟩. ⟨hal-02356810v2⟩
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