For the 2D stochastic Allen-Cahn equation, the Galerkin approximation converges in a negative Besov space with rate N^{-(α-δ)} for any α in (0,2/9) and δ>0.
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Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus
For the 2D stochastic Allen-Cahn equation, the Galerkin approximation converges in a negative Besov space with rate N^{-(α-δ)} for any α in (0,2/9) and δ>0.