Free Access
Issue
ESAIM: M2AN
Volume 55, Number 2, March-April 2021
Page(s) 507 - 531
DOI https://doi.org/10.1051/m2an/2020057
Published online 16 March 2021
  1. M. Bachmayr, A. Cohen and G. Migliorati, Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients. ESAIM:M2AN 51 (2017) 321–339. [CrossRef] [EDP Sciences] [Google Scholar]
  2. P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova and P. Wojtaszczyk, Convergence rates for greedy algorithms in reduced basis methods. SIAM J. Math. Anal. 43 (2011) 1457–1472. [CrossRef] [MathSciNet] [Google Scholar]
  3. P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova and P. Wojtaszczyk, Data assimilation in reduced modeling. SIAM/ASA J. Uncertainty Quantification 5 (2017) 1–29. [Google Scholar]
  4. A. Bonito, R. DeVore, D. Guignard, P. Jantsch and G. Petrova, Polynomial approximation of anisotropic analytic functions of several variables. Constructive Approximation (2020) 1–30. [Google Scholar]
  5. 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]
  6. A. Cohen and R. DeVore, Approximation of high-dimensional parametric PDEs. Acta Numer. 24 (2015) 1–159. [Google Scholar]
  7. A. Cohen and G. Migliorati, Multivariate approximation in downward closed polynomial spaces. In: Contemporary Computational Mathematics – A Celebration of the 80th Birthday of Ian Sloan. Springer (2018) 233–282. [Google Scholar]
  8. A. Cohen, W. Dahmnen, R. DeVore and J. Nichols, Reduced basis greedy selection using random training sets. ESAIM:M2AN 54 (2020) 1509–1524. [EDP Sciences] [Google Scholar]
  9. R. DeVore, Nonlinear approximation. Acta Numer. 7 (1998) 51–150. [Google Scholar]
  10. R. DeVore, G. Petrova and P. Wojtaszczyk, Greedy algorithms for reduced bases in Banach spaces. Constr. Approximation 37 (2013) 455–466. [Google Scholar]
  11. J.L. Eftang, A.T. Patera and E.M. Rønquist, An ``hp’’ certified reduced basis method for parametrized elliptic partial differential equations. SIAM J. Sci. Comput. 32 (2010) 3170–3200. [Google Scholar]
  12. Y. Maday and B. Stamm, Locally adaptive greedy approximations for anisotropic parameter reduced basis spaces. SIAM J. Sci. Comput. 35 (2013) A2417–A2441. [Google Scholar]
  13. Y. Maday, A.T. Patera, J. Penn and M. Yano, A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics. Int. J. Numer. Meth. Eng. 102 (2014) 933–965. [Google Scholar]
  14. G. Pisier, The Volume of Convex Bodies and Banach Space Geometry. Cambridge University Press 94 (1999). [Google Scholar]
  15. V. Temlykov, Nonlinear Kolmogorov widths. Math. Notes 63 (1998) 785–795. [Google Scholar]
  16. Z. Zou, D. Kouri and W. Aquino, An adaptive local reduced basis method for solving PDEs with uncertain inputs and evaluating risk. Comput. Methods Appl. Mech. Eng. 345 (2019) 302–322. [Google Scholar]

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