  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. Extensions to other variants of
adaptive collocation methods (including the classical one proposed in the paper
"Dimension-adaptive tensor-product quadratuture" Computing (2003) by T.
Gerstner and M. Griebel) is explored.
