Approximation of Probability Density Functions for PDEs with Random Parameters Using Truncated Series Expansions

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