# Lecture: Finite Elements

Lecturer: G. Kanschat A. Gilbert LSF Muesli

## Announcements

• The notes are online and will be augmented step by step.

## Homework assignments

We will prepare weekly homework assignments. The purpose of these assignments is training the subjects learned in class and developing an understanding for the taught concepts. The assignments 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. Students should present their results taking turns. Every student is expected to present at least once.

Handing in homework assignments is not mandatory in order to be allowed to take the exam. Nevertheless, passing the exam may be easier after completing them.

## Final exam

If the class does not exceed 20 participants, there will be oral exams of 20 minutes in the last week of the semester. Exam times will be scheduled in January.

## Literature

The class will mostly follow the books

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

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

• 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)