A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data, SIAM Journal on Numerical Analysis, vol.45, issue.3, pp.1005-1034, 2007. ,
DOI : 10.1137/050645142
Convergence of quasi-optimal stochastic Galerkin methods for a class of PDES with random coefficients , preprint EPFL, 2012. ,
On the Lebesgue constant of Leja sequences for the complex unit disk and of their real projection, preprint Laboratoire Jacques-Louis Lions, 2012. ,
High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs, preprint Laboratoire J.-L. Lions, to appear in Journ. Found. Comp. Math, 2013. ,
DOI : 10.1007/s10208-013-9154-z
URL : https://hal.archives-ouvertes.fr/hal-01350602
Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs, Foundations of Computational Mathematics, vol.60, issue.6, pp.615-646, 2010. ,
DOI : 10.1007/s10208-010-9072-2
Analytic regularity and polynomial approximation of parametric and stochastic PDE's, Analysis and Applications, pp.11-47, 2011. ,
Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs, ESAIM: Mathematical Modelling and Numerical Analysis, vol.47, issue.1, 2012. ,
DOI : 10.1051/m2an/2012027
Interpolation and Approximation, 1963. ,
Mathematical analysis and numerical methods for science and technology, 1992. ,
Nonlinear approximation, Acta Numerica, vol.41, issue.2, pp.51-150, 1998. ,
DOI : 10.1007/BF02274662
Optimal nonlinear approximation Manuscripta Math, p.469478, 1989. ,
Treatise on analysis, Volume I, Academic press, 1969. ,
Analytic regularity and nonlinear approximation of a class of parametric semilinear elliptic PDEs, Mathematische Nachrichten, vol.44, issue.6, 2013. ,
DOI : 10.1002/mana.201100131
Sparse Adaptive Approximation of High Dimensional Parametric Initial Value Problems, Vietnam Journal of Mathematics, vol.46, issue.5, 2013. ,
DOI : 10.1007/s10013-013-0011-9
Analytic regularity and GPC approximation for control problems constrained by linear parametric elliptic and parabolic PDEs, to appear in SIAM Journ, Contr. Optimization, 2013. ,
Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations, De Gruyter series in nonlinear analysis and applications, 1996. ,
Space-Time adaptive wavelet methods for parabolic evolution equations, Math. Comp, vol.78, issue.267, pp.1293-1318, 2009. ,
Nonlinear Kolmogorov width, Math. Notes 63-6, pp.785-795, 1998. ,
DOI : 10.1007/bf02312773
Convergence Rates of Sparse Chaos Approximations of Elliptic Problems with stochastic coefficients IMA Journ, Numer. Anal, vol.44, pp.232-261, 2007. ,