A Fully Discrete Implicit-Explicit Finite Element Method for Solving the FitzHugh-Nagumo Model (Journal of Computational Mathematics, 2020)
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-Nagumomodel from physiology. The first-order backward Euler discretization for the time derivative, and an implicit-explicit discretization for the nonlinear reaction term are employedfor 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-explicitfinite element method are proved, which shows that the FitzHugh-Nagumo model is accurately solved and the trajectory of potential transmission is obtained. The numericalresults are also reported to verify the convergence results and the stability of the proposedmethod.
Keywords: Finite element method; nonlinear reaction term; FitzHugh-Nagumo model; implicit-explicit scheme; stability and error estimates.