Numerical Methods for Partial Differential Equations
Lecturer: Dr. Clemens Pechstein| Time and Room (Lecture): | Tutorials |
|---|---|
| We 8.30 – 10.00, S2 053 | Mo 10.15 – 11.45, S2 054 |
| Th 8.30 – 10.00, S2 053 | |
| Lecture starts We, Oct. 3, 2012 | Tutorial starts Mo, Oct 8, 2012 |
Language: Englisch
Exam: To pass the lecture you have to attend an oral exam.
I warmly recommend to attend the tutorials as well. There we study the material of the lecture in more detail, and this usually helps a lot in understanding. Also, there is a practical part (of the tutorials), as we will implement some of the numerical methods on the computer.
Additional material (slides):
- Overview: classical vs. variational formulation
- Theorem 1.27: Banach's fixed point theorem
- The fixed point iteration behind the Lax-Milgram proof
- Element stiffness matrices, assembling
- Direct solvers for FEM systems
- Definition 1.48 - Lemma 1.51 (self-adjointness, eigenvalues, condition number)
- Convergence result for the method of steepest descent
- Overview of iterative solver algorithms
- Implementation of CG
- Convergence analysis of the improved Euler method
- Consistency analysis of implicit RKM
Additional literature:
- Walter Zulehner: Numerische Mathematik - Eine Einführung anhand von Differentialgleichungsproblemen. Band 1: Stationäre Probleme, Birkhäser, Basel, 2008.
- Walter Zulehner: Numerische Mathematik - Eine Einführung anhand von Differentialgleichungsproblemen. Band 2: Instationäre Probleme, Birkhäser, Basel, 2011.
- English lecture notes by Walter Zulehner (WS 2008)
Oral exam:
At the end of the winter semester I will fix some dates for oral exams for the majority as I guess most students want to pass the course soon. The remaining cases will be handled individually.
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last change:
2021-10-01
