A fully discrete C0 interior penalty Galerkin approximation of the extended Fisher–Kolmogorov equation

摘要

A fully discrete C0 interior penalty finite element method is proposed and analyzed for the Extended Fisher–Kolmogorov (EFK) equation ut+γΔ2u−Δu+u3−u=0 with appropriate initial and boundary conditions, where γ is a positive constant. We derive a regularity estimate for the solution u of the EFK equation that is explicit in γ and as a consequence we derive a priori error estimates that are robust in γ.