Numerical Methods for Hyperbolic and Kinetic Equations

What it is about

You will learn numerical methods for hyperbolic and kinetic partial differential equations. The module covers fundamental discretization procedures (e.g., finite differences, finite volumes, semi-Lagrangian) for hyperbolic conservation laws and methods for high-dimensional kinetic equations as well as asymptotic-preserving methods and applications in control and uncertainty quantification. In the end you will understand the connections between mathematical structure and practical implementation and will be able to apply selected methods to applications.

What you will be able to do

• Fundamental understanding of central numerical methods for hyperbolic and kinetic PDEs
• Recognize the link between mathematical structure and implementation
• Apply the learned methods in selected practical examples
• Knowledge of modern approaches such as asymptotic-preserving methods and methods for control/uncertainty quantification

What the module consists of

• VorlesungVermittlung der theoretischen Grundlagen und numerischen Verfahren; Anregung zur eigenen Analyse und Literaturstudium
• Übungen/BeispieleApplication and deepening of the presented methods through exercises

Teaching method

• Tafelvortrag und Folienfor structured presentation of the contents
• Aufgaben/Übungenfor deepening and application of what is learned
• Eigenstudium relevanter Literaturfor independent analysis and deepening