Klioba, KatharinaKatharinaKliobaSeifert, ChristianChristianSeifert2026-05-272026-05-272026-05-15Journal of Evolution Equations 26: 69 (2026)https://hdl.handle.net/11420/63211In this paper, we present an abstract framework to obtain convergence rates for the approximation of random evolution equations corresponding to a random family of forms determined by finite-dimensional noise. The full discretization error in space, time, and randomness is considered, where polynomial chaos expansion (PCE) is used for the semi-discretization in randomness. The main result are regularity conditions on the random forms under which convergence of polynomial order in randomness is obtained depending on the smoothness of the coefficients and the Sobolev regularity of the initial value. In space and time, the same convergence rates as in the deterministic setting are achieved. To this end, we derive error estimates for vector-valued PCE as well as a quantified version of the Trotter–Kato theorem for form-induced semigroups. We apply the abstract framework to an anisotropic diffusion model with random diffusion coefficients.en1424-32022026Springerhttps://creativecommons.org/licenses/by/4.0/Abstract Cauchy problemapproximationpolynomial chaos expansionconvergence ratesstrongly continuous semigroupsParabolic PDEsrandom coefficients47D0647N4065J0835K9041A25Natural Sciences and Mathematics::519: Applied Mathematics, ProbabilitiesNatural Sciences and Mathematics::518: Numerical AnalysisNatural Sciences and Mathematics::515: AnalysisJournal Article2026-05-26https://doi.org/10.15480/882.1719310.1007/s00028-025-01158-710.15480/882.17193