Uncertainty quantification by PDE-based models
We study the numerical treatment of PDE-based differential models which contain uncertain data (such as the right-hand sides or the coefficients of the equations, the boundary conditions or the shape of the domain), represented by suitable stochastic variables. The goal is the computation of quantities of statistical interest in a more efficient way than resorting to Monte-Carlo techniques. Based on such expansions as Karhunen-Loeve or Polynomial Chaos, we use Galerkin or collocation schemes in the stochastic variables. Specific attention is posed to the curse of dimensionality for these variables. We consider applications to fluid-dynamics and diffusion problems in porous media.