## Uncertainty Quantification for the solution of partial differential equations with uncertain parameters

**Organizers:**

Prof. Dr. Vincent Heuveline

Dr. Michael Schick

**Location:**

INF 294, Room -104

**Date:**

Tuesdays, 14:00 - 16:00 pm.

**Description:**

Many physical problems can be modeled by partial differential equations. These typically require parameters to be defined, values of which are often not known in a precise way. For example, consider a heat distribution on a plate, which can be modeled by a linear partial differential equation. Parameters in this model are the heat conductivity and boundary conditions of the problem. If they are assumed to be uncertain, then the heat distribution on the plate will be uncertain, too. Therefore it has stochastic characteristics, which need to be quantified appropriately.

Such "parametric uncertainties" may arise for example by measurement errors for parameter data or incomplete system knowledge. The major task of "uncertainty quantification" is to provide mathematical methods for modeling these uncertainties as random variables or random processes/fields and to quantify their effect on the solution of the underlying physical problem. This requires special numerical methods and appropriate model reduction techniques.

**Language:**

English or German is both fine for presentations (beamer) and the written seminar work. However, the material for preparation of the seminar topics provided by the organizers is in English.

**Formalities:**

In this seminar, 12 different topics are provided. Each interested student can create a list of three topics of his choice (prioritized). The 12 topics will be distributed as good as possible. **The maximum number of students is 12.** Therefore, if more students should be interested the topics will be distributed by random selection of the students which attend the **preliminary discussion on 3rd February 2015.** Later applications can only be considered if not all topics have been distributed.

**Preliminary discussion:**

Tuesday, 03.02.2015, INF 293 (URZ building), Room 101, 16:30 - 17:30 pm.

**Prerequisites:**

- Knowledge in numerical mathematics (linear systems and partial differential equations)
- Knowledge in stochastic (random variables, probability densities, stochastic processes)
- Knowledge in programming is optional
- Knowledge in functional analysis is helpful