  The probability density function (PDF) of a random variable associated with
the solution of a partial differential equation (PDE) with random parameters is
approximated using a truncated series expansion. The random PDE is solved using
two stochastic finite element methods, Monte Carlo sampling and the stochastic
Galerkin method with global polynomials. The random variable is a functional of
the solution of the random PDE, such as the average over the physical domain.
The truncated series are obtained considering a finite number of terms in the
Gram-Charlier or Edgeworth series expansions. These expansions approximate the
PDF of a random variable in terms of another PDF, and involve coefficients that
are functions of the known cumulants of the random variable. To the best of our
knowledge, their use in the framework of PDEs with random parameters has not
yet been explored.
