Lecturer: Max GUNZBURGER, Florida State University, Florida, USA Webpage: http://people.sc.fsu.edu/~mgunzburger/ Title: NUMERICAL METHODS FOR SPDE Date and time: Mon, April 29 to Fri, May 3, 2013 (Wednesday, May 1st is a Bank holiday in Spain. for this reason the new schedule for this course is as follows: April 29 (9-12h), April 30 (9-11h),May 1 (holiday), May 2 (9-12h), May 3 (9-11h) Abstract: The course provides and introduction to numerical methods for the approximate solutions of partial differential equations that have random inputs, e.g., forcing functions, coefficients, boundary data, domain definition, etc. Both random field and random parameter type inputs are considered. The topics considered could include: - Introductory remarks and definition of forward and inverse problems - Approximation of white and colored random fields - Stochastic Galerkin methods - Spectral approximations - Collocation approximations - Sampling methods - Surrogate approximation methods - Sparse grid methods - Local polynomial approximations - Wavelet approximation methods - Control, optimization, and identification problems The course is oriented towards graduate students having a basic background in numerical analysis and with some familiarity with PDEs; the statistical and probabilistic aspects will be largely self contained Bibliography: [1] D Xiu, Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton University Press, 2010 [2] Manas K. Deb, Ivo M. Babuška, J.Tinsley Oden, Solution of stochastic partial differential equations using Galerkin finite element techniques, Computer Methods in Applied Mechanics and Engineering, Volume 190, Issue 48, 28 September 2001, Pages 6359-6372 [3] I. Babuska, F. Nobile, R. Tempone, A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data, SIAM Review, Volume 52, Issue 2, pp. 317-355, 2010 [4] F. Nobile, R. Tempone and C. Webster A sparse grid stochastic collocation method for partial differential equations with random input data , SIAM J. Numer. Anal., 2008, vol. 46/5, pp. 2309--2345. [5] J. MIng and M. Gunzburger, Efficient Numerical Methods for Stochastic Partial Differential Equations Through Transformation to Equations Driven by Correlated Noise, International Journal for Uncertainty Quantification