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For semilinear stochastic evolution equations whose coefficients are moregeneral than the classical global Lipschitz, we present results on the strongconvergence rates of numerical discretizations. The proof of them provides anew approach to strong convergence analysis of numerical discretizations for alarge family of second order parabolic stochastic partial differentialequations driven by space-time white noises. We apply these results to thestochastic advection-diffusion-reaction equation with a gradient term andmultiplicative white noise, and show that the strong convergence rate of afully discrete scheme constructed by spectral Galerkin approximation andexplicit exponential integrator is exactly $\frac12$ in space and $\frac14$ intime. Compared with the optimal regularity of the mild solution, it indicatesthat the spetral Galerkin approximation is superconvergent and the convergencerate of the exponential integrator is optimal. Numerical experiments supportour theoretical analysis.

Strong convergence of numerical discretizations for semilinear stochastic evolution equations driven by multiplicative white noise