Numerical Study of a Particle Method for Gradient Flows

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Abstract

We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting scheme preserves the gradient flow structure at the particle level, and enables us to obtain a gradient descent formulation after time discretisation. We give several simulations to illustrate the validity of this method, as well as a detailed study of one-dimensional aggregation-diffusion equations.

Bibliographical metadata

Original languageEnglish
Pages (from-to)613-641
Number of pages29
JournalKinetic and Related Models
Volume10
Issue number3
Early online date31 Dec 2016
DOIs
StatePublished - 2016