A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure (Communications in Computational Physics, 2018)
We propose a positivity preserving entropy decreasing finite volume schemefor nonlinear nonlocal equations with a gradient flow structure. These properties allowfor accurate computations of stationary states and long-time asymptotics demonstratedby 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 timescales including metastability, as well as concentrations and self-similar behavior inducedby singular nonlocal kernels. We use the scheme to explore properties of theseequations beyond their present theoretical knowledge.