Free Access
Volume 51, Number 1, January-February 2017
Page(s) 321 - 339
Published online 23 December 2016
  1. 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] [Google Scholar]
  2. J. Beck, F. Nobile, L. Tamellini and R. Tempone, On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods. Math. Model. Methods Appl. Sci. 22 (2012) 1–33. [CrossRef] [Google Scholar]
  3. J. Beck, F. Nobile, L. Tamellini and R. Tempone, Convergence of quasi-optimal stochastic Galerkin methods for a class of PDEs with random coefficients. Comput. Math. Appl. 67 (2014) 732–751. [Google Scholar]
  4. 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] [Google Scholar]
  5. 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. [Google Scholar]
  6. A. Cohen, Numerical analysis of wavelet methods. Studies in Mathematics and its Applications. Elsevier, Amsterdam (2003). [Google Scholar]
  7. A. Cohen, R. DeVore and C. Schwab, Analytic regularity and polynomial approximation of parametric and stochastic PDEs. Anal. Appl. 9 (2011) 11–47. [Google Scholar]
  8. A. Cohen and R. DeVore, Approximation of high-dimensional parametric PDEs. Acta Numerica 24 (2015) 1–159. [CrossRef] [MathSciNet] [Google Scholar]
  9. R. DeVore, Nonlinear Approximation. Acta Numerica 7 (1998) 51–150. [CrossRef] [Google Scholar]
  10. R.G. Ghanem and P.D. Spanos, Spectral techniques for stochastic finite elements. Arch. Comput. Methods Eng. 4 (1997) 63–100. [Google Scholar]
  11. R.G. Ghanem and P.D. Spanos, Stochastic Finite Elements: A Spectral Approach, 2nd edition. Dover (2007). [Google Scholar]
  12. C.J. Gittelson, An adaptive stochastic Galerkin method for random elliptic operators. Math. Comput. 82 (2013) 1515–1541. [Google Scholar]
  13. O. Knio and O. Le Maitre, Spectral Methods for Uncertainty Quantication: With Applications to Computational Fluid Dynamics. Springer (2010). [Google Scholar]
  14. C. Schwab and R. Stevenson, Space-time adaptive wavelet methods for parabolic evolution equations. Math. Comput. 78 (2009) 1293–1318. [Google Scholar]
  15. 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). [Google Scholar]
  16. D. Xiu, Numerical methods for stochastic computations: a spectral method approach. Princeton University Press (2010). [Google Scholar]

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