Finite Element Methods (Winter Semester 2021/22)
- Lecturer: Prof. Dr. Willy Dörfler
- Classes: Lecture (0110300), Problem class (0110310)
- Weekly hours: 4+2
- Audience: Mathematics (from 7. semester)
If you are interested to attend the lecture, please send an email to
Sukhova, M <mariia.sukhova@kit.edu> .
You will then also get the password for the Ilias page.
We will start the lecture on 18.10, 12:00. Please note that the 3G-rules will be controlled. I will decide on the further procedure depending on the situation, eg the number of participants. Please inform us if you want to attend the lecture but cannot come.
The first exercise class will be on 27.10.
Please note the mail from the president from 6.10.2021 Corona Update: Studienbetrieb am KIT// Corona Update: Studies at KIT with an english version in the second half of the mail.
| Schedule | |||
|---|---|---|---|
| Lecture: | Monday 12:00-13:30 | 20.30 SR 3.69 | Begin: 18.10.2021 |
| Tuesday 14:00-15:30 | 20.30 SR 3.69 | ||
| Problem class: | Wednesday 16:00-17:30 | 20.30 SR 3.69 | |
| Lecturers | ||
|---|---|---|
| Lecturer, Problem classes | M. Sc. Mariia Sukhova | |
| Office hours: by appointment | ||
| Room 3.010 Kollegiengebäude Mathematik (20.30) | ||
| Email: mariia.sukhova@kit.edu | ||
Content
The topic of the course is to provide knowledge in numerically solving elliptic boundary value problems using the finite element method. We first present some basics like the weak formulation of these boundary value problems.
Then we study the finite element approach, in its various aspects, such as grid generation, choice of ansatz spaces, data structures for implementation, numerical integration, error estimates, a posteriori error estimates and solution techniques for the resulting systems of equations. A finite element solver in Matlab is provided to also get some practical experience.
Preliminary table of contents
01 Variational equations
02 Ritz-Galerkin method
03 Linear finite elements
04 Quadratic elements
05 Tensorproduct elements
06 Interpolation estimates
07 Special topics
08 Example of a finite element implementation
09 p and hp finite elements
10 Saddle Point Problems
Examination
There will be an oral examinations after the lecture time.
The examination language is either German or English.
References
Braess, D: Finite Elemente. Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie.
Braess, D: Finite Elements: Theory, fast solvers, and applications in solid mechanics.
Brenner, SC and Scott, LR: The mathematical theory of finite element methods.
Ciarlet, PG: The finite element method for elliptic problems.
Dörfler, W: Accompanying Lecture Notes.