TY - JOUR
T1 - A Fully Discrete Implicit-Explicit Finite Element Method for Solving the FitzHugh-Nagumo Model
AU - Cai , Li
AU - Sun , Ye
AU - Jing , Feifei
AU - Li , Yiqiang
AU - Shen , Xiaoqin
AU - Nie , Yufeng
JO - Journal of Computational Mathematics
VL - 3
SP - 469
EP - 486
PY - 2020
DA - 2020/03
SN - 38
DO - http://doi.org/10.4208/jcm.1901-m2017-0263
UR - https://global-sci.org/intro/article_detail/jcm/15796.html
KW - Finite element method, nonlinear reaction term, FitzHugh-Nagumo model, implicit-explicit scheme, stability and error estimates.
AB - <p style="text-align: justify;">This work develops a fully discrete implicit-explicit finite element scheme for a parabolic-ordinary system with a nonlinear reaction term which is known as the FitzHugh-Nagumo
model from physiology. The first-order backward Euler discretization for the time derivative, and an implicit-explicit discretization for the nonlinear reaction term are employed
for the model, with a simple linearization technique used to make the process of solving equations more efficient. The stability and convergence of the fully discrete implicit-explicit
finite element method are proved, which shows that the FitzHugh-Nagumo model is accurately solved and the trajectory of potential transmission is obtained. The numerical
results are also reported to verify the convergence results and the stability of the proposed
method.</p>