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Mixed finite element method for the nonlinear time-fractional stochastic fourth-order reaction-diffusion equation. (English) Zbl 1524.65570

Summary: 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 BDF \(2-\theta\) 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.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C10 Biomechanics
74K15 Membranes
74L15 Biomechanical solid mechanics
78A20 Space charge waves
92C37 Cell biology
92C05 Biophysics
76Q05 Hydro- and aero-acoustics

Software:

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References:

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