Solving the steady state diffusion equation with uncertainty

The goal of this project is to efficiently solve a steady state diffusion equation with a random coefficient. Although, such equations can be solved using Monte-Carlo methods, the lengthy computation time can be constraining. Using a Karhunen-Loéve expansion allows the random coefficient to be approximated with a finite sum of random variables. This expansion combined with a Galerkin method or stochastic collocation method reduces computation time.