A novel linearized Galerkin finite element scheme with fractional Crank–Nicolson method for the nonlinear coupled delay subdiffusion system with smooth solutions

A second order accurate linearized fractional Crank–Nicolson–Galerkin finite element scheme is proposed for solving the nonlinear coupled delay subdiffusion system. The scheme presented in this paper has the advantage of making iterative processes redundant. Existence and uniqueness results for the fully discrete solution are analyzed in detail. Further, a priori bound and convergence estimate for the fully discrete solution are derived in L^∞(L²) norm. Finally, we perform our numerical experiments on one- and two-dimensional problems to demonstrate the accuracy and efficiency of the proposed scheme.