# Lecture WS 24/25 Numerical Algorithms

## Uncertainty quantification of PDE with random input data

The numerical solution of linear partial differential equations (PDE) is well understood up to almost arbitrary accuracy if the input data of these equations are available up to arbitrary accuracy. However, in engineering applications this is not the case due to measurement errors in physical constants or tolerances in production processes, which makes the input data uncertain. This uncertainty propagates through the PDE and makes the solution of the PDE itself uncertain, making the use of highly accurate numerical approximation methods questionable. In the lecture we will discuss appropriate mathematical formalisms for PDE subject to uncertain input data and numerical algorithms which can quantify this uncertainty in terms of statistical moments such as the mean or the (co)variance.