Convergence of adaptive stochastic collocation with finite elements

@article{Feischl2020ConvergenceOA,
  title={Convergence of adaptive stochastic collocation with finite elements},
  author={M. Feischl and Andrea Scaglioni},
  journal={ArXiv},
  year={2020},
  volume={abs/2008.12591}
}
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove for the first time convergence of a stochastic collocation algorithm which adaptively enriches the parameter space as well as refines the finite element meshes. 

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