Mixed finite element method for a nonlinear fourth-order reaction-diffusion problem with fractional derivative

To solute the nonlinear fourth-order reaction-diffusion problem with time fractional derivative, some second-order time discrete schemes covering parameter θcombined with Galerkin finite element method are proposed and analyzed. At time t_k- θ( θ∈0,1/2), some second-order θschemes combined with weighted and shifted Grunwald difference (WSGD) approximation of fractional derivative are used to discrete the time direction, and the Galerkin finite element method is used to discretize the space direction. Through detailed discussion and analysis, the unconditional stability of the method is derived, and the prior error estimation is given. It is proved that the error results can achieve second-order accuracy in time.