Numerical Analysis for Stochastic Time-Space Fractional Diffusion Equation Driven by Fractional Gaussian Noise (Journal of Computational Mathematics, 2024)
In this paper, we consider the strong convergence of the time-space fractional diffusion equation driven by fractional Gaussian noise with Hurst index $H ∈ (1/2, 1).$ A sharpregularity estimate of the mild solution and the numerical scheme constructed by finite element method for integral fractional Laplacian and backward Euler convolution quadraturefor Riemann-Liouville time fractional derivative are proposed. With the help of inverseLaplace transform and fractional Ritz projection, we obtain the accurate error estimates intime and space. Finally, our theoretical results are accompanied by numerical experiments.