https://github.com/federicostra/conservationlawsparticles.jl

Particle methods for 1D conservation laws
https://github.com/federicostra/conservationlawsparticles.jl

analysis conservation-laws differential-equations differential-evolution mathematical-analysis mathematics numerical-analysis numerical-differential-equations numerical-discretization numerical-method

Last synced: about 1 month ago
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Particle methods for 1D conservation laws

• Host: GitHub
• URL: https://github.com/federicostra/conservationlawsparticles.jl
• Owner: FedericoStra
• License: mit
• Created: 2020-07-28T15:28:42.000Z (over 4 years ago)
• Default Branch: master
• Last Pushed: 2024-05-06T00:38:56.000Z (8 months ago)
• Last Synced: 2024-11-06T06:03:44.190Z (about 2 months ago)
• Topics: analysis, conservation-laws, differential-equations, differential-evolution, mathematical-analysis, mathematics, numerical-analysis, numerical-differential-equations, numerical-discretization, numerical-method
• Language: Julia
• Homepage:
• Size: 10.5 MB
• Stars: 1
• Watchers: 2
• Forks: 0
• Open Issues: 3
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

Awesome Lists containing this project

README

        
# ConservationLawsParticles.jl

![Lifecycle](https://img.shields.io/badge/lifecycle-maturing-blue.svg)

[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://FedericoStra.github.io/ConservationLawsParticles.jl/stable)

[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://FedericoStra.github.io/ConservationLawsParticles.jl/dev)

[![Build Status](https://github.com/FedericoStra/ConservationLawsParticles.jl/workflows/CI/badge.svg)](https://github.com/FedericoStra/ConservationLawsParticles.jl/actions)

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[![ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://img.shields.io/badge/ColPrac-Contributor's%20Guide-blueviolet)](https://github.com/SciML/ColPrac)

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](https://doi.org/10.1137/21M1462994).

> arXiv: [https://arxiv.org/abs/2107.10760](https://arxiv.org/abs/2107.10760).

You can cite the article as

```bibtex

@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)

```bibtex

@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},

}

```