Volume 17, Issue 1
A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure

Jos´e A. Carrillo ,  Alina Chertock and Yanghong Huang

10.4208/cicp.160214.010814a

Commun. Comput. Phys., 17 (2015), pp. 233-258.

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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.

  • History

Published online: 2018-04

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