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arXiv · 1512.03029

Numerical Study of a Particle Method for Gradient Flows

J. A. Carrillo·Y. Huang·F. S. Patacchini·G. Wolansky
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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.

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J. A. Carrillo, Y. Huang, F. S. Patacchini, G. Wolansky. 2015-12-09. Numerical Study of a Particle Method for Gradient Flows. https://doi.org/10.3934/krm.2017025

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