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Numerical Study of a Particle Method for Gradient Flows

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.

preprint2016arXivOpen access
J. A. CarrilloY. HuangF. S. PatacchiniG. Wolansky
math.APmath.NA
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Open access4 authors2 topics
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J. A. CarrilloY. HuangF. S. PatacchiniG. Wolansky

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