Volume 51, Number 1, January-February 2017
|Page(s)||321 - 339|
|Published online||23 December 2016|
- M. Bachmayr, A. Cohen, R. DeVore and G. Migliorati, Sparse polynomial approximation of parametric elliptic PDEs. Part II: Lognormal coefficients. ESAIM: M2AN 51 (2017) 341–363. [CrossRef] [EDP Sciences]
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- A. Chkifa, A. Cohen, R. DeVore and C. Schwab, Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs. ESAIM: M2AN 47 (2013) 253–280. [CrossRef] [EDP Sciences]
- A. Chkifa, A. Cohen and C. Schwab, Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs. J. Math. Pures Appl. 103 (2015) 400–428. [CrossRef]
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- R.G. Ghanem and P.D. Spanos, Stochastic Finite Elements: A Spectral Approach, 2nd edition. Dover (2007).
- C.J. Gittelson, An adaptive stochastic Galerkin method for random elliptic operators. Math. Comput. 82 (2013) 1515–1541. [CrossRef]
- O. Knio and O. Le Maitre, Spectral Methods for Uncertainty Quantication: With Applications to Computational Fluid Dynamics. Springer (2010).
- C. Schwab and R. Stevenson, Space-time adaptive wavelet methods for parabolic evolution equations. Math. Comput. 78 (2009) 1293–1318. [CrossRef]
- H. Tran, C. Webster and G. Zhang, Analysis of quasi-optimal polynomial approximations for parametric PDEs with deterministic and stochastic coefficients. Preprint arXiv:1508.01821 (2015).
- D. Xiu, Numerical methods for stochastic computations: a spectral method approach. Princeton University Press (2010).
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