Finite element methods, WS 2020/21

Persons  Contents  Organisation

Online course

The course mainly takes place online. Please register in ILIAS for this course. All relevant information are given there.

Persons

• Prof. Dr. Marlis Hochbruck (lectures)
• M.Sc. Constantin Carle (problem classes)
• M.Sc. Benjamin Dörich (problem classes)
• (problem classes)

Weekly hours

4 SWS lecture + 2 SWS problem class/tutorial; 8 ECTS points

Contents and Prerequisites

Contents: This lecture provides an introduction to the theory of finite element methods for elliptic boundary value problems in dimension one and two. In particular, stability and convergence will be proved and concepts for the implementation of such methods will be explained. Moreover, the numerical solution of elliptic eigenvalue problems will be investigated.
If time permits, we conclude with an introduction to Discontinuous Galerkin finite element methods.

Prerequisites: The students are expected to be familiar with the basics of numerical analysis, in particular interpolation, numerical integration, solution of linear systems and eigenvalue problems. Some basic knowledge in functional analysis and the analysis of boundary value problem is helpful but the main results will be repeated in the lecture.

Organisation

• Lecture: Videos of the lectures to single topics will be provided weekly in ILIAS. Further, there will be a weekly online session (live) with short repetitions and where questions can be asked to the content of the lectures.
• Problem classes/tutorials: Excercise sheets with solutions will be provided every week. Some exercises should be solved independently at home, others together in small groups during the exercises, either online or in seminar rooms.

Schedule

Tuesday,    16:00-17:00,    online 'Question & Answer' session for lectures
Thursday,    10:00-11:30,    problem classes: on-site (SR 3.068/3.069, building 20.30) and online
The online sessions take place in Zoom, the links to these sessions can be found in the ILIAS course.

Literature

• S. Brenner, R. Scott, The Mathematical Theory of Finite Element Methods, Springer Texts in Appl. Mathematics, Vol 15, Springer-Verlag, 3rd ed., 2008
• D. Braess, Finite Elements, Cambridge University Press, 3rd ed., 2007 (also available in German)

Further literature for Finite Element methods can be found in the ILIAS course.