Error Estimation and Adaptivity for Stochastic Collocation Finite Elements Part II: Multilevel Approximation

A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The extends the a posteriori error estimation framework introduced by Guignard and Nobile 2018 [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 Part I work [A. Bespalov, D. Silvester, F. Xu, SIAM Sci. Comput., 44 (2022), A3393–A3412]. Results potentially more efficient strategy, where meshes individually tailored, discussed herein. demonstrate that optimal convergence rates can be achieved, only when specific types problems. codes used generate numerical available on GitHub.