On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion

Convergence of an adaptive collocation method for the parametric stationary diffusion equation with finite-dimensional affine coefficient is shown. The algorithm relies on a recently introduced residual-based reliable posteriori error estimator. For convergence proof, strategy used stochastic Galerkin hierarchical estimator transferred to setting. Extensions other variants methods (including now classical approach proposed in [T. Gerstner and M. Griebel, Computing, 71 (2003), pp. 65--87]) are explored.