C. Bernardi and Y. Maday, Polynomial interpolation results in Sobolev spaces, Journal of Computational and Applied Mathematics, vol.43, issue.1-2, pp.53-80, 1992.
DOI : 10.1016/0377-0427(92)90259-Z

R. Bojanovic and R. A. Devore, On polynomials of best one side approximation, L'enseignement mathématique, 1966.

Y. Bourgault, D. Broizat, and P. Jabin, Convergence rate for the method of moments with linear closure relations, Kinetic and Related Models, vol.8, issue.1, pp.1-27, 2015.
DOI : 10.3934/krm.2015.8.1

Y. Brenier, R??solution d'??quations d'??volution quasilin??aires en dimension N d'espace ?? l'aide d'??quations lin??aires en dimension N + 1, Journal of Differential Equations, vol.50, issue.3, pp.375-390, 1983.
DOI : 10.1016/0022-0396(83)90067-0

Y. Brenier, L 2 Formulation of Multidimensional Scalar Conservation Laws, Archive for Rational Mechanics and Analysis, vol.72, issue.123, pp.1-19, 2009.
DOI : 10.1007/s00205-009-0214-0
URL : https://hal.archives-ouvertes.fr/hal-00101596

C. Canuto and A. Quarteroni, Approximation Results for Orthogonal Polynomials in Sobolev Spaces Math, pp.67-86, 1982.

B. Despres, D. Lucor, and G. Poette, Robust Uncertainty Propagation in Systems of Conservation Laws with the Entropy Closure Method, chapter, Uncertainty Quantification in Computational Fluid Dynamics, LNCSE 92, 2010.

D. Gottlieb and D. Xiu, Galerkin Method for Wave Equations with Uncertain Coefficients, Commun . Comp. Phys, vol.3, pp.505-518, 2008.

J. D. Jakeman, M. S. Eldred, and K. Sargsyan, Enhancing <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msub><mml:mrow><mml:mi>???</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-minimization estimates of polynomial chaos expansions using basis selection, Journal of Computational Physics, vol.289, pp.18-34, 2015.
DOI : 10.1016/j.jcp.2015.02.025

S. Jin, D. Xiu, and X. Zhu, Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings, Journal of Computational Physics, vol.289, pp.35-52, 2015.
DOI : 10.1016/j.jcp.2015.02.023

S. Jin, D. Xiu, and X. Zhu, A well balanced stochastic galerkin method for scalar conservation laws with random inputs, preprint 2015

M. Kand and A. Vasseur, Criteria on contraction for entropic discontinuities of the system of conservation laws via weighted relative entropy, 2015.

G. Lin, C. Su, and G. E. Karniadakis, The stochastic piston problem, Proceedings of the National Academy of Sciences, vol.101, issue.45, pp.15840-15845, 2004.
DOI : 10.1073/pnas.0405889101

P. Lions, B. Perthame, and E. Tadmor, A kinetic formulation of multidimensional scalar conservation laws and related equations, Journal of the American Mathematical Society, vol.7, issue.1, pp.7-8, 1994.
DOI : 10.1090/S0894-0347-1994-1201239-3

G. Meinardus, Approximation of functions: theory and numerical methods, 1967.
DOI : 10.1007/978-3-642-85643-3

B. Perthame, Kinetic formulation of conservation laws, of Oxford Lecture Series in Mathematics and its Applications, 2002.
URL : https://hal.archives-ouvertes.fr/hal-01146188

B. Perthame and E. Tadmor, A kinetic equation with kinetic entropy functions for scalar conservation laws, Communications in Mathematical Physics, vol.81, issue.3, pp.501-517, 1991.
DOI : 10.1007/BF02099071

. Ch, S. Schwab, J. Mishra, and . Sukys, Multi-level Monte Carlo finite volume methods for non-linear systems of conservation laws in multi-dimensions, Journal of Computational Physics, vol.231, issue.8, pp.3365-3388, 2012.

A. Weisse, G. Wellein, A. Alvermann, and H. Fehske, The kernel polynomial method, Reviews of Modern Physics, vol.78, 2006.

N. Wiener, The Homogeneous Chaos, American Journal of Mathematics, vol.60, issue.4, pp.897-936, 1938.
DOI : 10.2307/2371268