  A multiscale method is proposed for a parabolic stochastic partial
differential equation with additive noise and highly oscillatory diffusion. The
framework is based on the localized orthogonal decomposition (LOD) method and
computes a coarse-scale representation of the elliptic operator, enriched by
fine-scale information on the diffusion. Optimal order strong convergence is
derived. The LOD technique is combined with a (multilevel) Monte-Carlo
estimator and the weak error is analyzed. Numerical examples that confirm the
theoretical findings are provided, and the computational efficiency of the
method is highlighted.

Numerical Analysis;Numerical Analysis