Abstract:
We establish an optimal error estimate for a random particle blob method for the Keller-Segel equation in $mathbb{R}^d~(dgeq 2)$. With a blob size $varepsilon=h^{q_1}$ $(1/2frac{d}{1-q_1})$ norm up to a small probability $h^{C|ln h|}$, where $h$ is the initial grid size. |