Galerkin finite element method for time-fractional stochastic diffusion equations. (English) Zbl 1432.65153
Summary: In this paper, Galerkin finite element method for solving the time-fractional stochastic diffusion equations with multiplicative noise is proposed and investigated. The pathwise regularity properties of solutions to the semidiscrete Galerkin approximations are demonstrated and the convergence of optimal rates are derived. And also we construct the fully discrete scheme which is based on the approximations of the Mittag-Leffler function and analyze the error estimates of convergence in \(L_{2}\)-norm space. Finally, numerical results are conducted to confirm our theoretical findings.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 65M75 | Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
Keywords:
time-fractional derivative; stochastic diffusion equations; Galerkin finite element method; error estimatesReferences:
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