A partitioned finite element method for power-preserving discretization of open systems of conservation laws

Authors

Flávio Luiz Cardoso-Ribeiro, Denis Matignon, Laurent Lefèvre

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.

Citation

• Journal: IMA Journal of Mathematical Control and Information
• Year: 2021
• Volume: 38
• Issue: 2
• Pages: 493–533
• Publisher: Oxford University Press (OUP)
• DOI: 10.1093/imamci/dnaa038

BibTeX

@article{Cardoso_Ribeiro_2020,
  title={{A partitioned finite element method for power-preserving discretization of open systems of conservation laws}},
  volume={38},
  ISSN={1471-6887},
  DOI={10.1093/imamci/dnaa038},
  number={2},
  journal={IMA Journal of Mathematical Control and Information},
  publisher={Oxford University Press (OUP)},
  author={Cardoso-Ribeiro, Flávio Luiz and Matignon, Denis and Lefèvre, Laurent},
  year={2020},
  pages={493--533}
}

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