Mixed finite element method for the nonlinear time-fractional stochastic fourth-order reaction-diffusion equation

摘要

The nonlinear time-fractional stochastic fourth-order reaction-diffusion equation perturbed by noises is considered by the mixed finite element method in this paper. Based on the mixed finite element in spatial direction and the generalized BDF2 - theta in temporal discretization, the semi- and fully-discrete schemes are obtained. Further, the error estimates for the semi- and fully-discretizations and the regularity of solution are derived by some important lemmas. The numerical experiment is conducted to further confirm the theoretical results. (C) 2020 Elsevier Ltd. All rights reserved.