Open Access
Issue |
ESAIM: M2AN
Volume 54, Number 5, September-October 2020
|
|
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Page(s) | 1509 - 1524 | |
DOI | https://doi.org/10.1051/m2an/2020004 | |
Published online | 16 July 2020 |
- 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]
- 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]
- A. Buffa, Y. Maday, A.T. Patera, C. Prud’homme, G. Turinici, A priori convergence of the Greedy algorithm for the parameterized reduced basis. ESAIM: M2AN 46 (2012) 595–603. [CrossRef] [EDP Sciences] [Google Scholar]
- A. Chkifa, A. Cohen, G. Migliorati, F. Nobile and R. Tempone, Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDEs. ESAIM: M2AN 49 (2015) 815–837. [CrossRef] [EDP Sciences] [Google Scholar]
- 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]
- A. Cohen and R. DeVore, Approximation of high-dimensional PDEs. Acta Numer. 24 (2015) 1–159. [Google Scholar]
- 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]
- 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, Cham (2018) 233–282. [CrossRef] [Google Scholar]
- R. DeVore, G. Petrova and P. Wojtaszczyk, Greedy algorithms for reduced bases in Banach spaces. Constr. Approx. 37 (2013) 455–466. [Google Scholar]
- Y. Maday, A.T. Patera and G. Turinici, A priori convergence theory for reduced-basis approximations of single-parametric elliptic partial differential equations. J. Sci. Comput. 17 (2002) 437–446. [Google Scholar]
- Y. Maday, A.T. Patera and G. Turinici, Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations. C. R. Acad. Sci. Paris Sér. I Math. 335 (2002) 289–294. [Google Scholar]
- A.T. Patera, C. PrudÕhomme, D.V. Rovas and K. Veroy, A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations, In: Proc. 16th AIAA Computational Fluid Dynamics Conference (2003). [Google Scholar]
- G. Pisier, The Volume of Convex Bodies and Banach Spaces Geometry. Cambridge University Press (1989). [CrossRef] [Google Scholar]
- G. Rozza, D.B.P. Huynh and A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations application to transport and continuum mechanics. Arch. Comput. Methods Eng. 15 (2008) 229–275. [Google Scholar]
- S. Sen, Reduced-basis approximation and a posteriori error estimation for many-parameter heat conduction problems. Numer. Heat Transfer B-Fund 54 (2008) 369–389. [CrossRef] [Google Scholar]
- V.N. Temlyakov, The Marcinkiewicz-type discretization theorems. Constr. Approx. 48 (2018) 337–369. [Google Scholar]
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