The course will be held as hybrid teaching in summer term 2022. This means that it is possible - within the bouindaries of the of the applicable Corona regulations - to attend the lecture live in lecture hall L1|01 K328. In addition, participation will be possible via Zoom and video recordings will be published.
On Tuesday, Apr. 12th, 2022 at 12:30 pm, there will be a pre-meeting via Zoom only. The link for this will be posted via Moodle.
The first lecture will be held on Tuesday, Apr. 19th, 2022 at 12:30 pm. More information will follow via Moodle.
The following teaching materials or services will be provided:
- Script (English),
- Lecture notes/video of previous years (English)
- Lecture notes/video of the current semester
- Office hours (online)
Content:
- What are high accuracy/high order Methods?
- Discontinuous Galerkin Methods: approximation with Polynomials
- scalar conservation laws, weak formulation
- numerical fluxes
- temporal discretization
- Systems of equations and higher derivatives
- Poisson equation
- incompressible flows: Stokes and Navier-Stokes
- compressible Euler equations
- Basics on numerical analysis
- Consistency, Stability and Convergence
- Simulation of flows
- Exercices
- elementary programming in C#
- implementation of DG-Schemes using the BoSSS toolbox (see also https://github.com/FDYdarmstadt/BoSSS)
Literature:
* J. S. Hesthaven, T. Warburton: Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications; Springer, 2008.
* D. A. Di Pietro, A. Ern: Mathematical Aspects of Discontinuous Galerkin Methods, Springer, 2011.
* R. Hartmann: Numerical Analysis of Higher Order Discontinuous Galerkin Finite Element Methods; lecture notes, http://ganymed.iwr.uni-heidelberg.de/~hartmann/publications/2008/Har08b.pdf .
* R. Hartmann: Discontinuous Galerkin methods for compressible flows: higher order accuracy, error estimation and adaptivity; lecture notes http://ganymed.iwr.uni-heidelberg.de/~hartmann/publications/2005/Har05b.pdf .
* B. Cockburn, On Discontinuous Galerkin methods for convection-dominated problems; lecture notes, http://www.math.umn.edu/~bcockbur//LectureNotes.html.
Prequisites:
* Basic knowledge in parial differential equations and numerics.
* For Exercises: basic programming knowledge in some object-oriented language is helpful (e.g. C#, Java, Python, C++)
Expected Attendants:
10
Further Grading Information:
- The date can still be changed in consultation with the students (will be fixed in the preliminary discussion ).
- Approx. 30% of the time is spent on practical exercises on the PC
- Exercise materials & script provided by Moodle
- Lecture and exercises held by Dr. Florian Kummer and Jakob Sebastian, MSc.
Official Course Description:
This course deals with the application of high accuracy discontinuous Galerkin methods (methods with high order of convergence) to computational fluid dynamics. There is a stepwise approach here: the method is first derived, or developed, in 1D and for scalar advection. This is extended over the course of the semester to the treatment of incompressible Navier-Stokes equations.
- Lehrende: Florian Kummer