Error estimates for the semidiscrete Galerkin approximations of the FitzHugh-Nagumo equations

摘要

L2 error estimates are obtained for the semidiscrete approximation of the FitzHugh-Nagumo equations with nonsmooth initial data. The equations consist of a nonlinear parabolic equation coupled with an ordinary differential equation. Smoothing due to the parabolic equation is used to show increased accuracy for the approximation for positive time.