Authors

Lorenzo Agostini, Michel Fournié, Ghislain Haine

Abstract

The numerical simulation of the inviscid Burgers’ equation is often hindered by spurious oscillations near discontinuities. To mitigate this issue, a viscous term can be introduced, leading to the viscous Burgers’ equation. In this work, port-Hamiltonian formulations for both the inviscid and the viscous Burgers’ equations are proposed, enabling a representation that incorporates both convective and dissipative effects. Boundary control and observation are naturally handled within this framework. Applying a dedicated finite element method, a finite-dimensional port-Hamiltonian system is derived. The relationship between time step, spatial resolution, and viscosity required to achieve numerical stability is analyzed. Numerical experiments validate the effectiveness of the approach.

Keywords

burgers’ equation, finite element method, numerical stability, port-hamiltonian systems, structure-preserving discretization

Citation

  • Journal: IFAC-PapersOnLine
  • Year: 2026
  • Volume: 60
  • Issue: 1
  • Pages: 109–114
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.ifacol.2026.09.019
  • Note: 27th International Symposium on Mathematical Theory of Networks and Systems MTNS 2026- Waterloo, Ontario, August 17-21, 2026

BibTeX

@article{Agostini_2026,
  title={{Discretization of the Burgers’ equation as a port-Hamiltonian system}},
  volume={60},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2026.09.019},
  number={1},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Agostini, Lorenzo and Fournié, Michel and Haine, Ghislain},
  year={2026},
  pages={109--114}
}

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References