Strong convergence with rates for discretizations of SPDEs with non-Lipschitz drift

Abstract: 

I discuss the convergence analysis for space-time discretizations of three nonlinear SPDEs: the stochastic Navier-Stokes equation, the stochastic Allen-Cahn equation, and the stochastic mean curvature flow of planar curves of graphs. Depending on the drift operator, optimal rates with respect to strong convergence are valid for errors on large subsets, or on the whole sample set.