arXiv:2611.13145v1 Announce Type: new Abstract: In this paper we analyze a residual-based a posteriori error estimation strategy and adaptive multilevel algorithms for a class of parametric elliptic PDEs, where the diffusion coefficient depends on countably many uncertainty parameters. Under a saturation assumption on the parametric approximation space, we propose a computable residual-based error estimator. We also introduce the notion of K-compatibility of finite element meshes, which ensures that only the triangulations with comparable mesh sizes are used, and incorporate this concept into the adaptive algorithm. We prove that the estimator is reliable and satisfies K-dependent stability and reduction properties. These results underpin our convergence analysis of the adaptive multilevel algorithm: we show that the algorithm drives both the a posteriori error estimator and the true approximation error to zero. Numerical experiments illustrate and confirm the theoretical findings.