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arXiv · 1402.4252

A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure

José A. Carrillo·Alina Chertock·Yanghong Huang
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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.

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José A. Carrillo, Alina Chertock, Yanghong Huang. 2014-08-01. A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure. https://doi.org/10.4208/cicp.160214.010814a

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