Dual-based {\itshape a posteriori} error estimate for stochastic finite element methods

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Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, methodology): “This kind of approach then makes sense in the context of adaptive approximation procedures [60, 74, 81, 127, 128].”
A compressed sensing approach for partial differential equations with random input data (2012, background): “To this end, anisotropic sparse grid schemes have been proposed and shown to potentially significantly reduce the number of required deterministic solver calls, Nobile et al. (2007); Ganapathysubramanian and Zabaras (2007).”
Generalized spectral decomposition method for solving stochastic finite element equations : Invariant subspace problem and dedicated algorithms (2008, methodology): “For details, the reader can refer to [4–9].”
Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems (2010, methodology): “They lead to accurate predictions and allow for a better control on numerical simulations through a posteriori error estimation and adaptive approximation [22, 33, 45, 46, 48].”