@Article{CiCP-17-233, author = {A. Carrillo , JoséChertock , Alina and Huang , Yanghong}, title = {A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure}, journal = {Communications in Computational Physics}, year = {2018}, volume = {17}, number = {1}, pages = {233--258}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.160214.010814a}, url = {http://global-sci.org/intro/article_detail/cicp/10957.html} }