  This paper is focused on the convergence analysis of an adaptive stochastic
collocation algorithm for the stationary diffusion equation with parametric
coefficient. The algorithm employs sparse grid collocation in the parameter
domain alongside finite element approximations in the spatial domain, and
adaptivity is driven by recently proposed parametric and spatial a posteriori
error indicators. We prove that for a general diffusion coefficient with
finite-dimensional parametrization, the algorithm drives the underlying error
estimates to zero. Thus, our analysis covers problems with affine and nonaffine
parametric coefficient dependence.
