ConservationLawsParticles.jl

Particle methods for 1D conservation laws.

This package implements the deterministic particle schemes described in the article

E. Radici, F. Stra: Entropy solutions of mildly singular non-local scalar conservation laws with congestion via deterministic particle method. SIAM Journal on Mathematical Analysis 55.3 (2023), pp. 2001-2041. DOI: https://doi.org/10.1137/21M1462994. arXiv: https://arxiv.org/abs/2107.10760.

You can cite the article as

@article{Radici-Stra-2023,
 author = {Radici, Emanuela and Stra, Federico},
 title = {Entropy solutions of mildly singular nonlocal scalar conservation
          laws with congestion via deterministic particle methods},
 journal = {SIAM Journal on Mathematical Analysis},
 volume = {55},
 number = {3},
 pages = {2001-2041},
 year = {2023},
 issn = {0036-1410, 1095-7154},
 doi = {10.1137/21M1462994},
 url = {https://epubs.siam.org/doi/10.1137/21M1462994},
 eprint = {2107.10760},
 eprinttype = {arxiv},
 eprintclass = {math.AP},
 keywords = {entropy solutions, nonlinear mobility, nonlocal interaction,
             deterministic particle method, Lagrangian discretization,
             numerical scheme},
 addendum = {MSC: 35L65, 65M12, 65M75},
}

The convergence rate of the scheme is studied (among other results) in the follow-up article

@article{Marconi-Radici-Stra-2024,
 author = {Marconi, Elio and Radici, Emanuela and Stra, Federico},
 title = {Stability of quasi-entropy solutions of non-local scalar
          conservation laws},
 journal = {Calculus of Variations and Partial Differential Equations},
 volume = {64},
 number = {3},
 pages = {},
 year = {2024},
 date = {2024-11-16},
 issn = {1432-0835},
 doi = {10.1007/s00526-024-02848-9},
 url = {https://link.springer.com/article/10.1007/s00526-024-02848-9},
 eprint = {2211.02450},
 eprinttype = {arxiv},
 eprintclass = {math.AP},
 keywords = {entropy solutions, conservation laws},
 addendum = {MSC: 35L65, 65M12},
}

Please refer to the documentation for additional ways to cite this work.

Example

Particles trajectories and time evolution of the densities of two interacting species.

See the "Examples" section in the stable or dev documentation for more.