Structure-preserving discretization of port-Hamiltonian plate models

TL;DR

This paper presents a structure-preserving discretization method for port-Hamiltonian plate models, combining existing mixed finite element techniques with new error estimates, validated through numerical simulations.

Contribution

It bridges the gap between mixed finite element methods and port-Hamiltonian systems, providing a rigorous framework for discretizing plate models while preserving their structure.

Findings

Discretization preserves port-Hamiltonian structure.

Numerical simulations confirm expected convergence behaviors.

New error estimates are conjectured based on existing schemes.

Abstract

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.