@Article{CiCP-17-1,
author = {José, Carrillo, A. and Chertock, Alina and Yanghong, Huang},
title = {A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure},
journal = {Communications in Computational Physics},
year = {2015},
volume = {17},
number = {1},
pages = {233--258},
abstract = {<p style="text-align: justify;">We propose a positivity preserving entropy decreasing finite volume scheme
for nonlinear nonlocal equations with a gradient flow structure. These properties allow
for accurate computations of stationary states and long-time asymptotics demonstrated
by suitably chosen test cases in which these features of the scheme are essential.
The proposed scheme is able to cope with non-smooth stationary states, different time
scales including metastability, as well as concentrations and self-similar behavior induced
by singular nonlocal kernels. We use the scheme to explore properties of these
equations beyond their present theoretical knowledge.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.160214.010814a},
url = {https://global-sci.com/article/80378/a-finite-volume-method-for-nonlinear-nonlocal-equations-with-a-gradient-flow-structure}
}