Local Discontinuous Galerkin Methods with Decoupled Implicit-Explicit Time Marching for the Growth-Mediated Autochemotactic Pattern Formation Model
Year: 2024
Author: Hui Wang, Hui Guo, Jiansong Zhang, Lulu Tian
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 1 : pp. 208–236
Abstract
In this paper, two fully-discrete local discontinuous Galerkin (LDG) methods are applied to the growth-mediated autochemotactic pattern formation model in self-propelling bacteria. The numerical methods are linear and decoupled, which greatly improve the computational efficiency. In order to resolve the time level mismatch of the discretization process, a special time marching method with high-order accuracy is constructed. Under the condition of slight time step constraints, the optimal error estimates of this method are given. Moreover, the theoretical results are verified by numerical experiments. Real simulations show the patterns of spots, rings, stripes as well as inverted spots because of the interplay of chemotactic drift and growth rate of the cells.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0217
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 1 : pp. 208–236
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Local discontinuous Galerkin methods implicit-explicit time-marching scheme error estimate growth-mediated autochemotactic pattern formation model.