On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion

Martin Eigel, Oliver Ernst, Björn Sprungk, Lorenzo Tamellini

Published 2020-08-17Version 1

Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a-posteriori error estimator. For the convergence proof, a strategy recently used for a stochastic Galerkin method with an hierarchical error estimator is transferred to the collocation setting.