A deterministic particle method for the porous media equation

2025/01/30 by Amina Amassad, Amassad, Amina, Zhou, Datong · 3 citations
Engineering · #Fluid Dynamics Simulations and Interactions #Numerical methods in engineering #Grouting, Rheology, and Soil Mechanics

paper · pdf · doi:10.48550/arxiv.2501.18745

Abstract

This paper deals with the deterministic particle method for the equation of porous media (with p = 2). We establish a convergence rate in the Wasserstein-2 distance between the approximate solution of the associated nonlinear transport equation and the solution of the original one. This seems to be the first quantitative rate for diffusion-velocity particle methods solving diffusive equations and is achieved using a novel commutator estimate for the Wasserstein transport map.

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• A deterministic particle approximation for a fourth-order equation
• Beyond Bayesian Inference: The Correlation Integral Likelihood Framework and Gradient Flow Methods for Deterministic Sampling
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