Sparse Tensor Discretization of Elliptic sPDEs SIAM, J. Sci. Comput, vol.31, pp.4281-4304, 2009. ,
Sparse Tensor Approximation of Parametric Eigenvalue Problems in Numerical Analysis of Multiscale Problems (I ,
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
Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations, SIAM Journal on Numerical Analysis, vol.42, issue.2, pp.800-825, 2004. ,
DOI : 10.1137/S0036142902418680
ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS, Mathematical Models and Methods in Applied Sciences, vol.22, issue.09, 2011. ,
DOI : 10.1142/S0218202512500236
High dimensional polynomial interpolation on sparse grids, Adv. Comput. Math, pp.12-16, 2000. ,
A priori convergence of the greedy algorithm for the parameterized reduced basis, pp.2-46, 2012. ,
On the Lebesgue constant of Leja sequences for the unit disk and its applications to multivariate interpolation, Journal of Approximation Theory, vol.163, issue.5, pp.163-168, 2011. ,
DOI : 10.1016/j.jat.2011.02.001
URL : https://hal.archives-ouvertes.fr/hal-00630929
Lagrange interpolation at real projections of Leja sequences for the unit disk, to appear in the Proceedings of the, 2012. ,
On the Lebesgue constant of Leja sequences for the complex unit disk and of their real projection, preprint Laboratoire Jacques-Louis Lions, Journal of Approximation Theory, 2012. ,
Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs, ESAIM: Mathematical Modelling and Numerical Analysis, vol.47, issue.1, pp.2-47, 2013. ,
DOI : 10.1051/m2an/2012027
Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs, Foundations of Computational Mathematics, vol.60, issue.6, pp.10-16, 2010. ,
DOI : 10.1007/s10208-010-9072-2
ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S, Analysis and Applications, vol.09, issue.01, pp.1-37, 2011. ,
DOI : 10.1142/S0219530511001728
The Growth of Polynomials Bounded at Equally Spaced Points, SIAM Journal on Mathematical Analysis, vol.23, issue.4, p.970983, 1992. ,
DOI : 10.1137/0523054
Interpolation and Approximation, 1963. ,
Computational aspects of polynomial interpolation in several variables, Mathematics of Computation, vol.58, issue.198, pp.705-727, 1992. ,
DOI : 10.1090/S0025-5718-1992-1122061-0
Todor: Finite elements for elliptic problems with stochastic coefficients Comp, Meth. Appl. Mech. Engg, vol.194, pp.205-228, 2005. ,
An adaptive stochastic Galerkin method, to appear in Math, 2012. ,
Dimension-adaptive tensor-product quadrature, 2003. ,
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
Analytic regularity and best N-term approximation of high dimensional parametric initial value problems, Vietnam Journal of Mathematics, 2013. ,
Sparse tensor Galerkin discretizations for parametric and random parabolic PDEs I: Analytic regularity and gpc-approximation, Seminar for Applied Mathematics, ETH Zürich ,
Analytic regularity and gpc approximation for parametric and random 2nd order hyperbolic PDEs, Analysis and Applications, 2012. ,
The stochastic finite element methods, 1992. ,
Méthodes numériques -Interpolation, 1959. ,
Solvability problems of bivariate interpolation I, Constructive Approximation, pp.153-169, 1986. ,
Analysis of Discrete $$L^2$$ L 2 Projection on Polynomial Spaces with Random Evaluations, Foundations of Computational Mathematics, 2011. ,
DOI : 10.1007/s10208-013-9186-4
Reduced basis method for linear elasticity problems with many parameters, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.51-52, pp.4812-4829, 2008. ,
DOI : 10.1016/j.cma.2008.07.002
High order Galerkin approximations for parametric, second order elliptic partial differential equations Report 2012-22, Seminar for Applied Mathematics, ETH Zürich ,
A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data, SIAM Journal on Numerical Analysis, vol.46, issue.5, pp.2309-2345, 2008. ,
DOI : 10.1137/060663660
An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data, SIAM Journal on Numerical Analysis, vol.46, issue.5, pp.2411-2442, 2008. ,
DOI : 10.1137/070680540
Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions, Doklady Akademii Nauk SSSR, vol.4, pp.240-243, 1963. ,