Partial Differential Equations with Uncertainty: the Stochastic input case

The main aim of applied numerical simulations is to derive predictions. Since these predictions are the basis for decision making it is natural to question their accuracy, specially because in most of the cases there is uncertainty in data of the problem to solve.

We consider numerical approximations of partial differential equations (PDE) with stochastic coefficients, which is one way to address uncertainty quantification for PDEs.

We discuss efficient discretization strategies, give convergence results and present numerical results.