Scattering-Passive Structure-Preserving Finite Element Method for the Boundary Controlled Transport Equation with a Moving Mesh

Authors

Jesus-Pablo Toledo-Zucco, Denis Matignon, Charles Poussot-Vassal

Abstract

A structure-preserving Finite Element Method (FEM) for the transport equation in one- and two-dimensional domains is presented. This Distributed Parameter System (DPS) has non-collocated boundary control and observation, and reveals a scattering-energy preserving structure. We show that the discretized model preserves the aforementioned structure from the original infinite-dimensional system. Moreover, we analyse the case of moving meshes for the one-dimensional case. The moving mesh requires less states than the fixed one to produce solutions with a comparable accuracy, and it can also reduce the overshoot and oscillations of Gibbs phenomenon produced when using the FEM. Numerical simulations are provided for the case of a one-dimensional transport equation with fixed and moving meshes.

Keywords

Transport phenomena; Finite Element Method; Boundary Control; Moving mesh

Citation

• Journal: IFAC-PapersOnLine
• Year: 2024
• Volume: 58
• Issue: 6
• Pages: 292–297
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2024.08.296
• Note: 8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2024- Besançon, France, June 10 – 12, 2024

BibTeX

@article{Toledo_Zucco_2024,
  title={{Scattering-Passive Structure-Preserving Finite Element Method for the Boundary Controlled Transport Equation with a Moving Mesh}},
  volume={58},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2024.08.296},
  number={6},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Toledo-Zucco, Jesus-Pablo and Matignon, Denis and Poussot-Vassal, Charles},
  year={2024},
  pages={292--297}
}

Download the bib file

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