A Finite Dimensional Approximation of the shallow water Equations: The port-Hamiltonian Approach

Authors

Ramkrishna Pasumarthy, Arjan van der Schaft

Abstract

We look into the problem of approximating a distributed parameter port-Hamiltonian system which is represented by a non-constant Stokes-Dirac structure. We here employ the idea where we use different finite elements for the approximation of geometric variables (forms) describing an infinite-dimensional system, to spatially discretize the system and obtain a finite-dimensional port-Hamiltonian system. In particular we take the example of a special case of the shallow water equations

Citation

Journal: Proceedings of the 45th IEEE Conference on Decision and Control
Year: 2006
Volume:
Issue:
Pages: 3984–3989
Publisher: IEEE
DOI: 10.1109/cdc.2006.377022

BibTeX

@inproceedings{Pasumarthy_2006,
  title={{A Finite Dimensional Approximation of the shallow water Equations: The port-Hamiltonian Approach}},
  DOI={10.1109/cdc.2006.377022},
  booktitle={{Proceedings of the 45th IEEE Conference on Decision and Control}},
  publisher={IEEE},
  author={Pasumarthy, Ramkrishna and van der Schaft, Arjan},
  year={2006},
  pages={3984--3989}
}

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References

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van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics vol. 42 166–194 (2002) – 10.1016/s0393-0440(01)00083-3
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