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

  • § Corresponding author: Xiuwei Yin

    § Corresponding author: Xiuwei Yin

The Project-sponsored by NSFC (11571071), Innovation Program of Shanghai Municipal Education Commission (12ZZ063)) and The Fundamental Research Funds for the Central Universities (17D310403)

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  • 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 $ H∈ (\frac{1}{2}, 1) $. 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.

    Mathematics Subject Classification: 60H15, 60H35, 65C30.

    Citation:

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  • Figure 1.  Convergence rates for the spatial discretization

    Figure 2.  Convergence rates for the differential $\alpha$

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