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Instructors: Dr.-Ing. Florian Peter Kummer
Event type:
Lecture
Org-unit: Dept. 16 - Mechanical Engineering
Displayed in timetable as:
Verf num StrömSimula
Subject:
Crediting for:
Hours per week:
3
Language of instruction:
German and English
Min. | Max. participants:
- | -
Digital Teaching:
The event will be held in SoSe 2021 as a digital teaching. The Digital Teaching starts in week 15. The first date is therefore Tuesday, 13 Apr. 2021 at 12:30 p.m. On this date a preliminary discussion will take place first. This meeting will be held via ZOOM, further information will be released on Moodle.
The following teaching materials or services are offered: Lecture Notes (English), lecture recording (English); Additional explanatory videos on selected topics (German) as well as online consultation hours by appointment.
Course Contents:
* Was 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.
Preconditions:
* 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++)
Further Grading Information:
* The date can still be changed in consultation with the students (will be fixed in the first lecture).
* 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 Juan Gutierrez, MSc.
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