Evolution equations are partial differential equations (PDEs) that describe evolution over time. To account for random perturbations, random coefficients or noise terms are added, often requiring a numerical solution. The contributions of this thesis are twofold. First, a joint convergence rate is presented for the approximation in randomness, space, and time using polynomial chaos for the random coefficients. Second, convergence rates for the pathwise uniform error in time are obtained for nonlinear stochastic PDEs in the hyperbolic Kato setting.
