Structure Preserving Discretisation on Staggered Grids

What it is about

You will learn principles and methods of structure-preserving discretisations for partial differential equations. Using finite differences on staggered grids and finite element methods, you will learn to design procedures such that fundamental properties of the PDEs (e.g., invariants or Hamiltonian structures) are preserved. In the end you will be able to apply these procedures to classical PDEs such as Maxwell’s or Euler’s equations and assess their advantages and limitations.

What you will be able to do

• Understand properties of structure-preserving numerical methods
• Master principles for deriving such methods
• Apply to finite differences on staggered grids and finite elements
• Understand the advantages and limits of the methods
• Apply the methods to Maxwell and Euler equations

What the module consists of

• VorlesungDelivery of content through lectures with illustrative examples and discussion

Teaching method

• Vorlesung / TafelarbeitExplanation of general principles, motivation for independent engagement and study of the literature as well as implementation
• SkriptSupport and reference work on the lecture content