TY - JOUR
T1 - Positivity-Preserving Local Discontinuous Galerkin Method for Pattern Formation Dynamical Model in Polymerizing Actin Flocks
AU - Guo , Xiuhui
AU - Tian , Lulu
AU - Yang , Yang
AU - Guo , Hui
JO - Journal of Computational Mathematics
VL - 4
SP - 623
EP - 642
PY - 2023
DA - 2023/02
SN - 41
DO - http://doi.org/10.4208/jcm.2108-m2021-0143
UR - https://global-sci.org/intro/article_detail/jcm/21408.html
KW - Pattern formation dynamical model, Local discontinuous Galerkin method, Positive-preserving technique, Semi-implicit Runge-Kutta method, Stiff source.
AB - <p style="text-align: justify;">In this paper, we apply local discontinuous Galerkin (LDG) methods for pattern formation dynamical model in polymerizing actin flocks. There are two main difficulties in designing effective numerical solvers. First of all, the density function is non-negative, and zero is an unstable equilibrium solution. Therefore, negative density values may yield blow-up solutions. To obtain positive numerical approximations, we apply the positivity-preserving (PP) techniques. Secondly, the model may contain stiff source. The most commonly used time integration for the PP technique is the strong-stability-preserving Runge-Kutta method. However, for problems with stiff source, such time discretizations may require strictly limited time step sizes, leading to large computational cost. Moreover, the stiff source any trigger spurious filament polarization, leading to wrong numerical approximations on coarse meshes. In this paper, we combine the PP LDG methods with the semi-implicit Runge-Kutta methods. Numerical experiments demonstrate that the proposed method can yield accurate numerical approximations with relatively large time steps.</p>