Scattering-Passive Structure-Preserving Finite Element Method for the Boundary Controlled Transport Equation with a Moving Mesh
<|reference_start|>Scattering-Passive Structure-Preserving Finite Element Method for the Boundary Controlled Transport Equation with a Moving Mesh: 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.<|reference_end|>
@article{toledo-zucco2024scattering-passive,
    title={Scattering-Passive Structure-Preserving Finite Element Method for the
  Boundary Controlled Transport Equation with a Moving Mesh},
    author={Jesus-Pablo Toledo-Zucco, Denis Matignon, Charles Poussot-Vassal},
    journal={arXiv preprint arXiv:2402.01232},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.01232},
    primaryClass={math.NA cs.NA cs.SY eess.SY}
}