A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure. (28th November 2014)

• Record Type: Journal Article
• Authors: Carrillo, José A.; Chertock, Alina; Huang, Yanghong
• Is Part Of: Communications in computational physics. Volume 17:Number 1(2015:Jan.)
• Page Start: 233
• Page End: 258
• Publication Date: 2014-11-28
• Subjects: 65M08, -- 35R09, -- 34B10; Finite-volume method, -- gradient flow, -- nonlinear nonlocal equations; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.160214.010814a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.