Infinite-dimensional stochastic Darcy equations, finite-dimensional Petrov-Galerkin approximations and a priori error estimates
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TALK
Prof. Marcus Sarkis (University Worcester), 14 June 2010, 10 a.m., BA9909
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.