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},
}