# Numerics of Elliptic Partial Differential Equations

The course "Numerics of elliptic partial differential equations" consists of one 2-hour lecture and one 2-hour exercise per week.

# News

• For the Matlab exercises please bring your laptop to class (or one laptop per group if applicable).
• Due to scheduling conflicts, the first exercise will take place on the 8.11.2018 at 16:15 in HeHo 22, room E.04. The first exercise sheet is already online. The second will be available sometime next week. Since 1.11.2018 is a holiday, both lecture and exercises are cancelled on that day. Thus, you have to prepare the 1st and 2nd exercise sheets till 8.11.2018 and we will discuss both. Consequently, the exercise session on 8.11 may take longer than usual.

# Content

Topics:

• Modelling with PDEs
• Theory and numerics of elliptic PDEs
• FDM
• FEM
• Non-conform methods
• MultiGrid
• A-posteriori error estimators

# Dates

 Lecture Th, 8-10 HeHo 22, E.04 Exercise Th, 16-18 HeHo 22, E.04

tba

# Exercise Sheets

Exercises will take place Thursdays, weekly. Exercises will be conducted by a "voting" system. At the beginning of each exercise you have to cross the exercise problems you are ready to present. For each problem a student will be selected at random to present their solution.

If the solution is mostly correct and the student can explain their solution (subject to judgement of the exercise supervisor), the student gets full points for all of the problems they crossed out on the sheet. Otherwise the student forfeits all of their points for that exercise.

There will be two categories of points: for theory problems and for programming (MATLAB) problems. You require 50% of each to be admitted to the exam.

No.           Sheet        Due

1.

Sheet1

8.11.18

2.Sheet28.11.18
3.Sheet315.11.18
4.Sheet422.11.18
5.

Sheet5

fem2d

29.11.18
6.

Sheet6

Material

6.12.18
7.Sheet713.12.18
8.Sheet820.12.18

# Literature

A. Quarteroni, R. Sacco, F. Saleri: Numerische Mathematik 2, Springer 2002

A.Tveito, R. Winther: Einführung in partielle Differentialgleichungen - Ein numerischer Zugang, Springer 2002

D. Braess: Finite Elemente, 2. Aufl., Springer 1997P.

Knabner, L. Angermann: Numerik partieller Differentialgleichungen, Springer 2000

S.C. Brenner, L.R. Scott: The Mathematical Theory of Finite Element Methods, 2nd edition, Springer 2002

Ch. Großmann, H.-G. Roos: Numerik partieller Differentialgleichungen, Teubner 1994

W. Hackbusch: Theorie und Numerik elliptischer Differentialgleichungen, Teubner 1996

A. Meister: Numerik linearer Gleichungssysteme, Vieweg 1999

G. Dzuik: Theorie und Numerik Partieller Differentialgleichungen, De Gruyter 2010

W. Arendt, K. Urban: Partielle Differenzialgleichungen, Spektrum 2010

L. C. Evans: Partial Differential Equations, 2nd edition, AMS 2010

# Responsible

• Lecture:
• Prof. Dr. Karsten Urban
• E-mail
• Helmholtzstr. 20
• Raum 1.12
• 0731/50-235 35
• Exercises:
• M. Sc. Mazen Ali
• E-mail
• Helmholtzstr. 20
• Raum 1.30
• 0731/50-235 38

# Exam and Requirements

Exam: tba.

To be admitted to the exam you have to actively participate at the exercises and achieve a minimum of 50% of all theory points and 50% of all coding points.