Error Estimation and Adaptivity for Stochastic Collocation Finite Elements Part I: Single-Level Approximation

A general adaptive refinement strategy for solving linear elliptic partial differential equations with random data is proposed and analysed herein. The extends the a posteriori error estimation framework introduced by Guignard Nobile [SIAM J. Numer. Anal., 56 (2018), pp. 3121--3143] to cover problems nonaffine parametric coefficient dependence. suboptimal, but nonetheless reliable convenient implementation of involves approximation decoupled PDE common finite element space. Computational results obtained using such single-level are presented in this paper (part I). Results potentially more efficient multilevel strategy, where meshes individually tailored, will be discussed part II work. codes used generate numerical available on GitHub.