Free Access
Issue
ESAIM: M2AN
Volume 51, Number 1, January-February 2017
Page(s) 321 - 339
DOI https://doi.org/10.1051/m2an/2016045
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]
  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]
  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. [CrossRef]
  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]
  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. [CrossRef]
  6. A. Cohen, Numerical analysis of wavelet methods. Studies in Mathematics and its Applications. Elsevier, Amsterdam (2003).
  7. A. Cohen, R. DeVore and C. Schwab, Analytic regularity and polynomial approximation of parametric and stochastic PDEs. Anal. Appl. 9 (2011) 11–47. [CrossRef] [MathSciNet]
  8. A. Cohen and R. DeVore, Approximation of high-dimensional parametric PDEs. Acta Numerica 24 (2015) 1–159. [CrossRef] [MathSciNet]
  9. R. DeVore, Nonlinear Approximation. Acta Numerica 7 (1998) 51–150. [CrossRef]
  10. R.G. Ghanem and P.D. Spanos, Spectral techniques for stochastic finite elements. Arch. Comput. Methods Eng. 4 (1997) 63–100. [CrossRef]
  11. R.G. Ghanem and P.D. Spanos, Stochastic Finite Elements: A Spectral Approach, 2nd edition. Dover (2007).
  12. C.J. Gittelson, An adaptive stochastic Galerkin method for random elliptic operators. Math. Comput. 82 (2013) 1515–1541. [CrossRef]
  13. O. Knio and O. Le Maitre, Spectral Methods for Uncertainty Quantication: With Applications to Computational Fluid Dynamics. Springer (2010).
  14. C. Schwab and R. Stevenson, Space-time adaptive wavelet methods for parabolic evolution equations. Math. Comput. 78 (2009) 1293–1318. [CrossRef]
  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).
  16. D. Xiu, Numerical methods for stochastic computations: a spectral method approach. Princeton University Press (2010).

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