Tutorials will start in the second week (October 26)
List of exercise sheets
Literature
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)
Homework assignments
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.
Programming
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.
Final exam
- 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.
