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

José A. Carrillo, Alina Chertock & Yanghong Huang

DOI: 10.4208/cicp.160214.010814a

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

Published online: 2018-04

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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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@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} }
TY - JOUR T1 - A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure AU - A. Carrillo , José AU - Chertock , Alina AU - Huang , Yanghong JO - Communications in Computational Physics VL - 1 SP - 233 EP - 258 PY - 2018 DA - 2018/04 SN - 17 DO - http://doi.org/10.4208/cicp.160214.010814a UR - https://global-sci.org/intro/article_detail/cicp/10957.html KW - AB -

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.

A. Carrillo , JoséChertock , Alina and Huang , Yanghong. (2018). A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure. Communications in Computational Physics. 17 (1). 233-258. doi:10.4208/cicp.160214.010814a
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