Optimal error estimates for fractional stochastic partial differential equation with fractional Brownian motion

Abstract

<p style='text-indent:20px;'>In this paper, we consider the numerical approximation for a class of fractional stochastic partial differential equations driven by infinite dimensional fractional Brownian motion with hurst index <inline-formula><tex-math id="M1">\begin{document}$ H∈ (\frac{1}{2}, 1) $\end{document}</tex-math></inline-formula>. By using spectral Galerkin method, we analyze the spatial discretization, and we give the temporal discretization by using the piecewise constant, discontinuous Galerkin method and a Laplace transform convolution quadrature. Under some suitable assumptions, we prove the sharp regularity properties and the optimal strong convergence error estimates for both semi-discrete and fully discrete schemes.