Many natural and engineered systems from weather patterns and ocean currents to biological processes, are governed by dynamics that are inherently uncertain or randomly influenced. Understanding these systems requires accurate simulation of complex equations that combine deterministic laws with random effects. Stochastic partial differential equations (SPDEs) provide the mathematical foundation for modeling such systems under uncertainty. One particularly important example is the stochastic Navier–Stokes equation, a probabilistic counterpart of the classical equation that underpins our understanding of fluid turbulence and remains an unsolved Millennium Prize Problem. This project develops rigorous and reliable numerical methods to approximate solutions of such SPDEs, addressing a key national need: predictive simulation tools that can operate robustly in uncertain, noisy, or data-limited environments. By improving the reliability of simulations in fields such as weather science, energy systems, and aerospace engineering, this work supports the NSF mission to advance science, promote national prosperity, and prepare a skilled STEM workforce. Technically, this project focuses on the development and analysis of finite element methods for nonlinear SPDEs with provable strong convergence. In particular, the research establishes error estimates in strong norms and investigates how solution regularity, noise structure, and discretization interact to determine convergence rates.