Structure-preserving discretization of port-Hamiltonian plate models

Andrea Brugnoli (1) , Daniel Alazard (1) , Valérie Pommier-Budinger (1) , Denis Matignon (2)

1 DCAS - Département Conception et conduite des véhicules Aéronautiques et Spatiaux
2 DISC - Département d'Ingénierie des Systèmes Complexes

Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and port-Hamiltonian systems has been carried out. In this paper we demonstrate how existing methods can be employed to discretize dynamical plate problems in a structure-preserving way. Based on convergence results of existing schemes, new error estimates are conjectured; numerical simulations confirm the expected behaviors.

Mots clés: Port-Hamiltonian systems; Kirchhoff Plate; Mindlin-Reissner Plate; Mixed Finite Element Method; Numerical convergence

Domaines: Autre

Andrea Brugnoli, Daniel Alazard, Valérie Pommier-Budinger, Denis Matignon. Structure-preserving discretization of port-Hamiltonian plate models. Mathematical Theory of Networks and Systems, Aug 2021, Cambridge, United Kingdom. pp.359-364, ⟨10.1016/j.ifacol.2021.06.094⟩. ⟨hal-03349680⟩