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On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
2020, Eigel, Martin, Ernst, Oliver, Sprungk, Björn, Tamellini, Lorenzo
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.