Advanced Topics in PDEs
Partial differential equations are frequently used to model and ultimately simulate physical phenomena. The important aspect with regard to the reliability and relevance of such a simulation is to take into account and to quantify uncertainties arising from unknown parameters and measurement errors. In this class, we will consider the modelling of uncertain parameters in the context of PDEs and introduce state of the art methods for the numerical computation of quantities of interest. In particular, we will address the famous multilevel Monte Carlo method and Bayesian parameter estimation techniques.
Introduction to Partial Differential Equations