Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations

Hui  Huang; Jian-Guo Liu

doi:10.3934/dcdsb.2016107

Article Contents

2016, Volume 21, Issue 10: 3463-3478. Doi: 10.3934/dcdsb.2016107

This issue Previous Article Global classical solutions for mass-conserving, (super)-quadratic reaction-diffusion systems in three and higher space dimensions Next Article The vanishing surface tension limit for the Hele-Shaw problem

Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations

Hui Huang^1, and
Jian-Guo Liu^2,

1.
Department of Mathematical Sciences, Tsinghua University, Beijing, 100084
2.
Department of Physics and Department of Mathematics, Duke University, Durham, NC 27708

Received: December 2015

Revised: September 2016

Published: December 2016

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Abstract

In this paper, we discuss error estimates associated with three different aggregation-diffusion splitting schemes for the Keller-Segel equations. We start with one algorithm based on the Trotter product formula, and we show that the convergence rate is $C\Delta t$, where $\Delta t$ is the time-step size. Secondly, we prove the convergence rate $C\Delta t^2$ for the Strang's splitting. Lastly, we study a splitting scheme with the linear transport approximation, and prove the convergence rate $C\Delta t$.

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Mathematics Subject Classification: Primary: 65M12, 65M15; Secondary: 92C17.

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