The probability density function (PDF) of a random variable associated with the solution of a stochastic partial differential equation (SPDE) is approximated using a truncated series expansion. The SPDE is solved using two stochastic finite element (SFEM) methods, Monte Carlo sampling and the stochastic Galerkin method with global polynomials. The random variable is a functional of the solution of the SPDE, 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 SPDEs has not yet been explored. 查看全文>>