Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus

08/25/2019

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by   Ting Ma, et al.

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In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations driven by space-time white noise on . First we prove that the convergence rate for stochastic 2D heat equation is of order α-δ in Besov space ^-α for α∈(0,1) and δ>0 arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations of order α-δ in ^-α for α∈(0,2/9) and δ>0 arbitrarily small.