TY - JOUR
T1 - Local Discontinuous Galerkin Methods with Decoupled Implicit-Explicit Time Marching for the Growth-Mediated Autochemotactic Pattern Formation Model
AU - Wang , Hui
AU - Guo , Hui
AU - Zhang , Jiansong
AU - Tian , Lulu
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 208
EP - 236
PY - 2023
DA - 2023/12
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0217
UR - https://global-sci.org/intro/article_detail/aamm/22296.html
KW - Local discontinuous Galerkin methods, implicit-explicit time-marching scheme, error estimate, growth-mediated autochemotactic pattern formation model.
AB - <p style="text-align: justify;">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.</p>