Stochastic Finite Element Methods

By M. A. Gutiérrez, S. Krenk. 2004

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Approximation of high-dimensional parametric PDEs * (2015, result): “We refer in particular to [40, 46, 55, 56, 90] for general introductions to these approaches, and to [1, 41, 37, 53, 54, 83, 84] for related work prior to the results exposed in our paper.”
Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs (2010, methodology): “…discretization in D. ∗This research was supported by the Office of Naval Research Contracts ONR-N00014-08-1-1113, ONR N0001405-1-0715; the ARO/DoD Contracts W911NF-05-1-0227 and W911NF-07-1-0185; the NSF Grant DMS-0810869; the Swiss National Science Foundation under Grant No. 200021-120290/1 1”
Uncertainty analysis of complex structural systems (2009, methodology): “Perturbation method Perturbation procedures have been used from the early developments of stochastic FE analyses [1].”
Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs (2011, background): “This is the point of view adopted for example in [1,2,13,15,19,22,23].”
Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDEs (2010, background): “This is the point of view adopted for example in [14, 16, 4, 13, 3, 18, 19].”