Local Discontinuous Galerkin Methods with Decoupled Implicit-Explicit Time Marching for the Growth-Mediated Autochemotactic Pattern Formation Model

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.

Author Details

Hui Wang

Hui Guo

Jiansong Zhang

Lulu Tian