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In this paper, we consider the strong convergence order of the exponentialintegrator for the stochastic heat equation driven by an additive fractionalBrownian motion with Hurst parameter $H\in(\frac12,1)$. By showing the strongorder one of accuracy of the exponential integrator under approprioteassumptions, we present the first super-convergence result in temporaldirection on full discretizations for stochastic partial differential equationsdriven by infinite dimensional fractional Brownian motions with Hurst parameter$H\in(\frac12,1)$. The proof is a combination of Malliavin calculus, the$L^p(\Omega)$-estimate of the Skorohod integral and the smoothing effect of theLaplacian operator.

Super-convergence analysis on exponential integrator for stochastic heat equation driven by additive fractional Brownian motion