Convergence of adaptive stochastic collocation with finite elements

08/28/2020

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by   Michael Feischl, et al.

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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 convergence of an adaptive algorithm which adaptively enriches the parameter space as well as refines the finite element meshes.