Numerical Methods for Stochastic Partial Differential Equations
Stochastic partial differential equations are PDEs with random coefficients. Sometimes this is used for evolutionary PDEs driven by white noise, a slightly different subject.
Many problems involve uncertain data, which may be modelled as random fields. The solution is then also a random field. Next to the obvious Monte Carlo methods, there is growing interest in direct approximations of the solution in a high-dimensional space, mainly by Galerkin and similar methods. The presentation will try to draw a parallel to the deterministic case, and outline the current state and open problems.
Hermann G. Matthies, Technische Universit�t Braunschweig, Germany