A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
Numerical Analysis
2015-06-18 v2
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.
Keywords
Cite
@article{arxiv.1402.4252,
title = {A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure},
author = {José A. Carrillo and Alina Chertock and Yanghong Huang},
journal= {arXiv preprint arXiv:1402.4252},
year = {2015}
}