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Numerical Methods for Partial Differential Equations (4V, 2Ü)
Dr. Max WinklerSS2019
Contents
Partial differential equations (PDEs) describe a countless number of phenomena in the natural sciences, such as heat conduction, the propagation of sound and electromagnetic waves the motion of fluids and the behavior of quantum physical particles. Their numerical solution (also known as simulation) is key for a deeper understanding.
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Goals of this class
Goals of this class are:
- getting to know the solution behavior of prototypical partial differential equations,
- to understand the properties (stability, error analysis) of fundamental solution methods (finite differences and finite elements)
- and to gather hands-on experience in solving partial differential equations.
- Analysis of Partial Differential Equations,
- Optimal Control of Partial Differential Equations,
- Functional Analysis.
What we expect from you
- Attend the lectures and the exercise each week.
- Repeat the theoretical findings of the lecture before each exercise. You should spend approximately 3 hours per week for this.
- Prepare for each exercise by trying to solve all tasks on your own.
- Solve the homework exercises, maybe in groups of 2 or 3 students. You should spend 5 hours per week for this.
- For the exercises and homework we will frequently use Matlab. However, this lecture is not a Matlab programming course. Depending on your prior knowledge you should spend a certain time in learning Matlab. It's worth it!
- Visit this website regularly to be informed on important News.
- If you did not understand something, ask your lecturer or attend the office hours of Dr. Winkler. Do not wait until the end of the semester.
News
| 25.03.2019 | First week of the semester:
Monday and Tuesday, there will be a lecture, the lecture on Wednesday will be canceled.
Please solve the exercises from the first exercise sheet by yourself during that time.
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| 05.03.2019 | The 2nd exercise (10.04.2019) will take place in the computer pool 41/738 |
| 06.03.2019 | Office ours Max Winkler: any time when present |
| 08.04.2019 | The lecture on Tuesday will take place at 7:30 in the room 2/N102. |
| 18.06.2019 19.06.2019 | The plan changes : The lecture and exercise at 18.6. and 19.6. is cancelled. Instead there is a prgramming exercise on Tuesday (18.6.) in the 3rd and 4th unit (11:30-14:00) in the computer pool 39/738. |
| 26.06.2019 03.07.2019 | The exercises on 26.06.2019 and 03.07.2019 will take place in the computer pool 39/738. |
Dates
| 3 Veranstaltungen aus dem Archiv des Vorlesungsverzeichnisses (Sommersemester 2019) | |||||
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| Nummer | Name | Gruppen | Dozenten | Zeit | Raum |
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220000-A05
[SS2019]
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Numerik partieller Differentialgleichungen
[Vorlesung]
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wo: B_MaIn6, B_Ph__6, M_MaFM2, M_MaIn2, M_MaMa2, M_MaTM2, M_MaWM2, B_Ph__5, M_MaFM4, M_MaIn4, M_MaMa4, M_MaTM4, M_MaWM4, B_MaFM6, B_MaMa6, B_MaTM6, B_MaWM6, M_MROp2, M_DS__2 |
Dr. Max Winkler (225033) |
Mittwoch (wö.) 07:30-09:00 |
2/B202 |
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220000-A05A
[SS2019]
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Numerik partieller Differentialgleichungen
[Vorlesung]
|
wo: B_MaIn6, B_Ph__6, M_MaFM2, M_MaIn2, M_MaMa2, M_MaTM2, M_MaWM2, B_Ph__5, M_MaFM4, M_MaIn4, M_MaMa4, M_MaTM4, M_MaWM4, B_MaFM6, B_MaMa6, B_MaTM6, B_MaWM6, M_MROp2, M_DS__2 |
Dr. Max Winkler (225033) |
Montag (wö.) 09:15-10:45 |
2/B202 |
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220000-A06
[SS2019]
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Numerik partieller Differentialgleichungen
[Übung]
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wo: B_MaIn6, B_Ph__6, M_MaFM2, M_MaIn2, M_MaMa2, M_MaTM2, M_MaWM2, B_Ph__5, M_MaFM4, M_MaIn4, M_MaMa4, M_MaTM4, M_MaWM4, B_MaFM6, B_MaMa6, B_MaTM6, B_MaWM6, M_MROp2, M_DS__2 |
Dr. Max Winkler (225033) |
Dienstag (wö.) 07:30-09:00 |
2/N102 |
Additional lecture material
- Beiblatt: Lagrange-Elemente
- Beiblatt: Einige lokale Formfunktionen
- Beiblatt: Einige globale Formfunktionen
- Beiblatt: Quadraturformeln
Tutorials
Exam
There will be an oral examination for participants after the end of the class.Supplementary References
Finite-Differenzen-Verfahren:- Grossmann, Roos: Numerische Behandlung partieller Differentialgleichungen, Teubner, 2005
- Grossmann, Roos, Stynes: Numerical Treatment of Partial Differential Equations, Springer, 2007; is available online at TU Chemnitz
- Jovanović, Süli: Analysis of Finite Difference Schemes, Springer, 2014
- Brenner, Scott: The Mathematical Theory of Finite Element Methods, Springer, 2008; is available online at TU Chemnitz
- Ciarlet: The Finite Element Method for Elliptic Problems, North-Holland, 1978; Reprint by SIAM, 2002
- Ern, Guermond: Theory and Practice of Finite Elements, Springer, 2004
- Braess: Finite Elemente -- Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie, Springer, 2007; is available online at TU Chemnitz
- Alt: Lineare Funktionalanalysis, Springer, 2012; is available online at TU Chemnitz
- Dobrowolski: Angewandte Funktionalanalysis, Springer, 2010; is available online at TU Chemnitz
- Thomée: From finite differences to finite elements: A short history of numerical analysis of partial differential equations, Journal of Computational and Applied Mathematics, 2001, Volume 128, Issues 1–2, Pages 1–54
Introductions to Matlab
We highly recommend to familiarize yourself (by participating in the labs, and by independent studies) with the basics in Matlab. This will be useful not only for this class. Find additional material on Matlab here. Documentation of the Matlab Toolboxes:- PDE Toolbox Online Documentation, MathWorks
- PDE Toolbox User's Guide (pdf-Version), MathWorks