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A Partitioned Finite Element Method for power-preserving discretization of open systems of conservation laws

Cardoso-Ribeiro, Flávio Luiz and Matignon, Denis and Lefèvre, Laurent A Partitioned Finite Element Method for power-preserving discretization of open systems of conservation laws. (2021) IMA Journal of Mathematical Control and Information, 38 (2). 493-533. ISSN 0265-0754

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Official URL: https://doi.org/10.1093/imamci/dnaa038

Abstract

This paper presents a structure-preserving spatial discretization method for distributed parameter port- Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and geometries. For these systems, a partitioned finite element method (PFEM) is derived, based on the integration by parts of one of the two conservation laws written in weak form. The non-linear one-dimensional shallow-water equation (SWE) is first considered as a motivation example. Then, the method is investigated on the example of the non-linear two-dimensional SWE. Complete derivation of the reduced finite-dimensional port-Hamiltonian system (pHs) is provided and numerical experiments are performed. Extensions to curvilinear (polar) coordinate systems, space-varying coefficients and higher-order pHs (Euler–Bernoulli beam equation) are provided.

Item Type:Article
HAL Id:hal-03149105
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Instituto Tecnologico de Aeronautica - ITA (BRAZIL)
Other partners > Université Grenoble Alpes - UGA (FRANCE)
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Deposited On:22 Feb 2021 16:28

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