Bath Institute For Complex Systems - ENS de Cachan - Antenne de ...

[6] P. G. Ciarlet. The finite element method for elliptic problems, volume 40 of Classics in AppliedMathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002.[7] K.A. Cliffe, M. B. Giles, R. Scheichl, and A. L. Teckentrup. Multilevel Monte Carlo methodsand applications to elliptic PDEs with random coefficients. Computing and Visualization inScience, 2011. accepted for publication.[8] G. Da Prato and J. Zabczyk. Stochastic equations in infinite dimensions, volume 44 of Encyclopediaof Mathematics and its Applications. Cambridge University Press, Cambridge, 1992.[9] M. Dashti and A. Stuart. Uncertainty quantification and weak approximation of an ellipticinverse problem. Technical Report arXiv:1102.0143, arXiv.org, 2010. Submitted to SIAMJournal on Numerical Analysis.[10] G. de Marsily, F. Delay, J. Goncalves, P. Renard, V. Teles, and S. Violette. Dealing withspatial heterogeneity. Hydrogeol. J, 13:161–183, 2005.[11] P. Delhomme. Spatial variability and uncertainty in groundwater flow param- eters, a geostatisticalapproach. Water Resourc. Res., pages 269–280, 1979.[12] P. Frauenfelder, C. Schwab, and R. A. Todor. Finite elements for elliptic problems withstochastic coefficients. Comput. Methods Appl. Mech. Engrg., 194(2-5):205–228, 2005.[13] J. Galvis and M. Sarkis. Approximating infinity-dimensional stochastic Darcy’s equationswithout uniform ellipticity. SIAM Journal on Numerical Analysis, 47:3624–3651, 2009.[14] R. G. Ghanem and P. D. Spanos. Stochastic finite elements: a spectral approach. Springer-Verlag, New York, 1991.[15] M. B. Giles. Improved multilevel Monte Carlo convergence using the Milstein scheme. volume256 of Monte Carlo and Quasi-Monte Carlo methods 2006, pages 343–358. Springer, 2007.[16] M. B. Giles. Multilevel Monte Carlo path simulation. Operations Research, 256:981–986, 2008.[17] C. J. Gittelson. Stochastic Galerkin discretization of the log-normal isotropic diffusion problem.Math. Models Methods Appl. Sci., 20(2):237–263, 2010.[18] W. Hackbusch. Elliptic differential equations: Theorey and numerical treatment, volume 18 ofSpringer Series in Computational Mathematics. Springer-Verlag, Berlin, 2010.[19] S. Heinrich. Multilevel Monte Carlo methods. volume 2179 of Lecture notes in ComputerScience, pages 3624–3651. Springer, Philadelphia, PA, 2001.[20] S. Zhang. Analysis of finite element domain embedding methods for curved domains usinguniform grids. SIAM Journal on Numerical Analysis, 46:2843–2866, 2008.29