Free Access
Issue
ESAIM: M2AN
Volume 47, Number 1, January-February 2013
Page(s) 253 - 280
DOI https://doi.org/10.1051/m2an/2012027
Published online 29 November 2012
  1. I. Babuska, R. Tempone and G.E. Zouraris, Galerkin finite element approximations of stochastic elliptic partial differential equations. SIAM J. Numer. Anal. 42 (2004) 800−825. [CrossRef] [MathSciNet]
  2. I. Babuška, F. Nobile and R. Tempone, A stochastic collocation method for elliptic partial differential equations with random input data. SIAM J. Numer. Anal. 45 (2007) 1005−1034. [CrossRef] [MathSciNet]
  3. C. Bernardi and R. Verfürth, Adaptive finite element methods for elliptic equations with non-smooth coefficients. Numer. Math. 85 (2000) 579−608. [CrossRef] [MathSciNet]
  4. P. Binev, W. Dahmen, and R. DeVore, Adaptive finite element methods with convergence rates. Numer. Math. 97 (2004) 219−268. [CrossRef] [MathSciNet]
  5. A. Buffa, Y. Maday, A.T. Patera, C. Prudhomme and G. Turinici, A priori convergence of the greedy algorithm for the parameterized reduced basis. ESAIM : M2AN 3 (2012) 595–603. [CrossRef] [EDP Sciences]
  6. A. Cohen, Numerical analysis of wavelet methods. Elsevier, Amsterdam (2003).
  7. A. Cohen, W. Dahmen and R. DeVore, Adaptive wavelet methods for elliptic operator equations – Convergence rates. Math. Comput. 70 (2000) 27−75. [CrossRef] [MathSciNet]
  8. A. Cohen, W. Dahmen and R. DeVore, Adaptive wavelet methods for operator equations – Beyond the elliptic case. J. FoCM 2 (2002) 203−245.
  9. A. Cohen, R. DeVore and C. Schwab, Convergence rates of best N-term Galerkin approximations for a class of elliptic sPDEs. Found. Comput. Math. 10 (2010) 615–646. [CrossRef] [MathSciNet]
  10. A. Cohen, R. DeVore and C. Schwab, Analytic regularity and polynomial approximation of parametric and stochastic PDE’s. Anal. Appl. 9 (2011) 11–47. [CrossRef] [MathSciNet]
  11. R. DeVore, Nonlinear approximation. Acta Numer. 7 (1998) 51–150. [CrossRef]
  12. W. Dörfler, A convergent adaptive algorithm for Poisson’s equation. SIAM J. Numer. Anal. 33 (1996) 1106–1124. [CrossRef] [MathSciNet]
  13. Ph. Frauenfelder, Ch. Schwab and R.A. Todor, Finite elements for elliptic problems with stochastic coefficients. Comput. Methods Appl. Mech. Eng. 194 (2005) 205–228. [CrossRef] [MathSciNet]
  14. T. Gantumur, H. Harbrecht and R. Stevenson, An optimal adaptive wavelet method without coarsening of the iterands. Math. Comput. 76 (2007) 615–629. [CrossRef] [MathSciNet]
  15. R. Ghanem and P. Spanos, Spectral techniques for stochastic finite elements. Arch. Comput. Methods Eng. 4 (1997) 63–100. [CrossRef]
  16. P. Grisvard, Elliptic problems on non-smooth domains. Pitman (1983).
  17. V.H. Hoang and Ch. Schwab, Sparse tensor Galerkin discretizations for parametric and random parabolic PDEs I : Analytic regularity and gpc-approximation. Report 2010-11, Seminar for Applied Mathematics, ETH Zürich (in review).
  18. V.H. Hoang and Ch. Schwab, Analytic regularity and gpc approximation for parametric and random 2nd order hyperbolic PDEs. Report 2010-19, Seminar for Applied Mathematics, ETH Zürich (to appear in Anal. Appl. (2011)).
  19. M. Kleiber and T.D. Hien, The stochastic finite element methods. John Wiley & Sons, Chichester (1992).
  20. R. Milani, A. Quarteroni and G. Rozza, Reduced basis methods in linear elasticity with many parameters. Comput. Methods Appl. Mech. Eng. 197 (2008) 4812–4829. [CrossRef]
  21. P. Morin, R.H. Nochetto and K.G. Siebert, Data oscillation and convergence of adaptive FEM. SIAM J. Numer. Anal. 38 (2000) 466–488. [CrossRef] [MathSciNet]
  22. F. Nobile, R. Tempone and C.G. Webster, A sparse grid stochastic collocation method for elliptic partial differential equations with random input data. SIAM J. Numer. Anal. 46 (2008) 2309–2345. [CrossRef] [MathSciNet]
  23. F. Nobile, R. Tempone and C.G. Webster, An anisotropic sparse grid stochastic collocation method for elliptic partial differential equations with random input data. SIAM J. Numer. Anal. 46 (2008) 2411–2442. [CrossRef] [MathSciNet]
  24. Ch. Schwab and A.M. Stuart Sparse deterministic approximation of Bayesian inverse problems. Report 2011-16, Seminar for Applied Mathematics, ETH Zürich (to appear in Inverse Probl.).
  25. Ch. Schwab and R.A. Todor, Karhúnen-Loève, Approximation of random fields by generalized fast multipole methods. J. Comput. Phys. 217 (2000) 100–122. [CrossRef] [MathSciNet]
  26. R. Stevenson, Optimality of a standard adaptive finite element method. Found. Comput. Math. 7 (2007) 245–269. [CrossRef] [MathSciNet]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you