Winter 2016/2017

Lecturer: | G. Kanschat |
---|---|

Assistants: | S. Meggendorfer |

Class data: | LSF, MÜSLI |

Lectures: |
Tue 14-16h, Mathematikon, SR A Thu 14-16h, Mathematikon, SR A |

Tutorials: |
Wed 11-13h, Mathematikon, Seminarraum 11 (engl) Fri 11-13h, Mathematikon, Seminarraum 10 (engl) |

- Overview over topics covered in this course
- Corrected version of Homework No. 12 online.
- Programming exam online
- Corrected Exercise 5.2 - there was a typo in the transformation formula.
- Please register via MÜSLI in one of the tutorials.
- Homeworks will be published on the website each Thursday. No return of solutions required.

- Exercise Sheet 1 (26.10.)
- Exercise Sheet 2 (02.11.)
- Exercise Sheet 3 (10.11.)
- Exercise Sheet 4 (17.11.)
- Exercise Sheet 5 (24.11.)
- Exercise Sheet 6 (01.12.)
- Exercise Sheet 7 (08.12.)
- Exercise Sheet 8 (15.12.)
- Exercise Sheet 9 (22.12.)
- Exercise Sheet 10 (11.01.)
- Exercise Sheet 11 (18.01.)
- Exercise Sheet 12 (26.01.)

The class will mostly follow the book

- Grossmann, Ch., Roos, H.-G., Stynes, M.: Numerical Treatment of Partial Differential Equations
- Grossmann, Ch., Roos: Numerische Behandlung partieller Differentialgleichungen (German)

Additional literature on the finite element method for elliptic partial differential equations:

- Lecture notes on Nitsche's method and discontinuous Galerkin methods, the a priori estimate for advection diffusion problems is here in the appendix.
- Johnson, C.: Numerical Solutions of Partial Differential Equations by the Finite Element Method (particularly good for beginners)
- Rannacher, R.: Skript Numerische Mathematik 2 (German)
- Brenner, S. C., Scott, L. R.: The Mathematical Theory of Finite Element Methods (covers solvers)
- Ciarlet, Ph. G.: The Finite Element Method for Elliptic Problems
- Verfürth, R.: Lecture notes Adaptive finite element methods

Further reading on elliptic PDE and Sobolev spaces:

- Alt, H. W.: Lineare Funktionalanalysis (German)
- Evans, L. C.: Partial differential equations
- Gilbarg, D., Trudinger, Neil S.: Elliptic Partial Differential Equations of Second Order
- Adams, R. A., Fournier, J. J. F.: Sobolev spaces (or first edition by Adams)

We will prepare weekly homework assignments. The purpose of these assigments is training the subjects learned in class and developing an understanding for the taught concepts. The assigments are essential for acquiring the competences taught in the class and tested in the final exam.

The homework assignments should be prepared in small groups discussing the steps of the solution. The groups should present their solutions during tutorial. There is no return of written solutions required.

The homework assignments will be discussed during the tutorials. There will be no points given and accumulated over the semester.

The task of solving partial differential equations in practice cannot effectively be done by hand - therefore we need the computational power of modern computing systems. If you are interested in solving PDE, you probably would like to have a look at the following C++ based software:

deal.II is a state-of-the-art open source finite element library supporting the creation of finite element codes and an open community of users and developers. It has a good and well structured tutorial with a lot of examples, that leads step-by-step through all features of the library.

Amandus is a simple experimentation suite built on the deal.II library. The purpose of Amandus is enabling the solution of PDE problems without much prior knowledge of C++ or deal.II. It basically allows the implementation of a new equation by just providing local integrators for residuals and matrices. In addition, it has a lot of example applications. A documentation can be found here.

If you are new in programming C++, you can find tutorials here in English 1 , English 2 and German.

- The written exam will take place
**Thursday, February 9th, 2pm sharp(!) in Mathematikon, SR A**for two hours. - Non-electronic help like books and notes is allowed. No phones, no electronic devices.
- Please bring enough paper for writing the exam.