The Multi-index Stochastic Collocation method for uncertainty quantification of PDEs with random parameters

In many real-life applications, one needs to solve partial differential equations (PDEs) to predict the behavior of a system, most often by numerical methods. This goal is often hampered by the fact that the parameters of the equations might be not known exactly, and modeled as random variables; one therefore would like to assess how this uncertainty propagates to the solution of the PDE. To this end, in this contribution we discuss the Multi-Index Stochastic Collocation (MISC) method, and show its effectiveness with on a numerical test.