Linearized Variable‐Time‐Step BDF3–VEM Scheme for Semilinear Parabolic Equations With Nonlinear Vanishing Delay

ABSTRACT In this paper, we study the numerical solution of semilinear parabolic equations with nonlinear vanishing delay, employing a linearized variable‐time‐step three‐step backward differentiation formula (vBDF3) for time discretization and the virtual element method (VEM) for spatial discretization. The proposed scheme is flexible for variable time steps and spatial meshes. Based on the technique of the discrete orthogonal convolution kernels, we establish the unconditional optimal ‐norm error estimate for the fully discrete solution through the error splitting technique. Finally, numerical experiments are given to demonstrate the high‐order accuracy and unconditional convergence of the linearized scheme.