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ConservationLawsParticles.jl

Lifecycle Stable Dev Build Status Code Style: Blue ColPrac: Contributor's Guide on Collaborative Practices for Community Packages

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{doi:10.1137/21M1462994,
    author = {Radici, Emanuela and Stra, Federico},
    title = {Entropy solutions of mildly singular non-local scalar conservation
             laws with congestion via deterministic particle method},
    journal = {SIAM Journal on Mathematical Analysis},
    volume = {55},
    number = {3},
    pages = {2001-2041},
    year = {2023},
    doi = {10.1137/21M1462994},
    URL = {https://doi.org/10.1137/21M1462994},
    eprint = {2107.10760},
    eprinttype = {arxiv},
    eprintclass = {math.AP},
}

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

@online{arxiv/2211.02450,
    author = {Marconi, Elio and Radici, Emanuela, and Stra, Federico},
    title = {Stability of quasi-entropy solutions of non-local scalar conservation laws},
    year = {2022},
    eprint = {2211.02450},
    eprinttype = {arxiv},
    eprintclass = {math.AP},
    url = {https://arxiv.org/abs/2211.02450},
}