A deterministic particle method for the porous media equation
Amina Amassad, Datong Zhou
TL;DR
This paper introduces a deterministic particle method for the porous media equation with p=2, providing a convergence rate in Wasserstein-2 distance and a novel commutator estimate, advancing numerical analysis of diffusive PDEs.
Contribution
It establishes the first quantitative convergence rate for diffusion-velocity particle methods solving porous media equations using a new commutator estimate.
Findings
First quantitative convergence rate in Wasserstein-2 distance
Novel commutator estimate for Wasserstein transport map
Applicable to diffusive equations with particle methods
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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Taxonomy
TopicsFluid Dynamics Simulations and Interactions · Numerical methods in engineering · Grouting, Rheology, and Soil Mechanics