Infinite-dimensional stochastic Darcy equations, finite-dimensional Petrov-Galerkin approximations and a priori error estimates

Prof. Marcus Sarkis

June 14, 2010, 10 a.m. BA 9909

In this talk we consider a stochastic Darcy's pressure equation with random log-normal permeability and random right-hand side. To accommodate the lack of ellipticity and continuity, and singular right-hand sides, we introduce an appropriate representation of the permeability stochastic fields and infinite-dimensional norms and spaces. We then introduce new continuous and discrete weak formulations based on a Petrov-Galerkin strategy and present inf-sup conditions, well-posedness, a priori error estimations and numerical experiments.