Error estimate of a random particle blob method for the Keller-Segel equation

Huang, Hui; Liu, Jian-Guo

doi:10.1090/mcom/3174

Error estimate of a random particle blob method for the Keller-Segel equation
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by Hui Huang and Jian-Guo Liu PDF

Math. Comp. 86 (2017), 2719-2744 Request permission

Abstract:

We establish an optimal error estimate for a random particle blob method for the Keller-Segel equation in $\mathbb {R}^d~(d\geq 2)$. With a blob size $\varepsilon =h^{\kappa }$ $(1/2<\kappa <1)$, we prove a rate $h|\ln h|$ of convergence in $\ell ^p_h$ $(p>\frac {d}{1-\kappa })$ norm up to a probability $1-h^{C|\ln h|}$, where $h$ is the initial grid size.

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