Numerik III

News and Important Remarks

• You can have a look on your Klausur on friday, 19.10. between 11.00 and 14.00 o'clock in Arnimallee 6, room 131 (Secretary Nordt).

• Here you can find the corrected results of the Nachklausur.

• The Nachklausur on saturday, 13.10.2012 takes place in Arnimallee 6 SR 032, it starts at 10:15 o'clock and lasts 90 minutes. Please arrive at least 15 minutes in advance in front of the main entrance.

• Attention: the date for the Nachklausur is shifted to saturday, 13.10.2012.

• You can have a look on your Klausur on thursday, 19.7. between 10.00 and 14.00 o'clock in Arnimallee 6, room 131 (Secretary Nordt).

• Here you can find the results of the Klausur.

• The Klausur on tuesday, 10.7.2012 takes place in Arnimallee 6 SR 032, it starts at 16:15 o'clock and lasts 90 minutes. Please arrive at least 10 minutes in advance. Pleace bring a valid identity card or passport with you and put it out on your desk in the beginning. You are allowed to use all your written documents, books, and a non-programmable calculator. Please do not use a pencil.

• Attention: the constants in problem 2b) on exercise sheet 9 are incorrect. Exercise 9 (corrected version)

• The problems 4 and 5 of erxercise sheet 6 are postponed till Thursday the 7'th June.

• Since Thursday the 17'th of May is a holiday, there will be an ersatz tutorial taking place on Wednesday the 16'th, 10-12 o'clock in Takustr.9, SR 049.

• On April 12, 2012 a lecture will take place instead of a tutorial. The tutorials start a week later, at April 19, 2012.

Dates

General Information

Description

Mathematical modelling of spatial or spatial/temporal phenomena such as porous medium flow, solidification of melts, weather prediction, etc. typically leads to partial differential equations (pdes). After some remarks on the modelling with and classification of pdes, the course will concentrate on elliptic problems. Starting with a brief introduction to the classical theory (existence and uniqueness of solutions, Green's functions) and assiciated difference methods we will mainly focus on weak solutions and their approximation by finite element methods. Adaptivity and multigrid methods will be also discussed.

Target Audience

Students of the Diploma, Bachelor, Master and BMS course of studies

Prerequisites:

Basics of calculus (Analysis I, II, III), linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

Registration

All participants should register at the KVV which is our only data base for organizing this course. Registration at KVV is mandatory to participate in the written exams (Klausur and Nachklausur). The number of registrations in KVV is also used to justify rooms etc. for this course.

In addition, depending on your program of study, you have to register in the following way:

• BMS students have to register via e-mail at the one-stop office.
• Studierende im Campus Management verwalteter Bachelor- und Masterstudiengänge müssen sich eigenverantwortlich und verbindlich über das Campus Management an- bzw. abmelden. Über Möglichkeiten und Pflichten zur An- und Abmeldung gibt die Homepage des Campus Managements Auskunft. Für Fragen ist ferner eine Hotline unter 838-77777 sowie eine E-Mail-Adresse cm-hotline@fu-berlin.de eingerichtet.
• Für Studierende der Bioinformatik alter Studienordnung ist die Anmeldung im KVV verbindlich. Im Fall eines Rücktritts ist die Abmeldung bis 31.10.2011 im KVV erforderlich.
• Die Anmeldung im KVV ist für Diplom- und Staatsexamenskandidaten alter Studienordnung (nicht Bachelor/Master) ausreichend. Im Falle eines Rücktritts ist keine Abmeldung nötig.

Exercises and Criteria for a Certificate

Tutorial & Exercises

• Exercises will be handed out each Tuesday during the lecture. These exercises are also available electronically on this web page (see below). The first release takes place on April 17, 2012.
• The tutorial offers the possibility to ask questions regarding the presented material. Furthermore future and previous exercises are discussed in the tutorial. The first tutorial takes place on Thursday, April 19, 2012. To our experience, active participation in the tutorial is not only fundamental for the understanding of the presented material but also for a successful Klausur.
• The exercises are intended to be solved by teams of two to three members. Please remember to annotate the name of all participating team members on the completed exercises.
• The solutions have to be finished before the tutorial on Thursday at 12 o'clock in the week after they were handed out. Please put your exercises into the box with the name 'Wolf' on it, found in the first floor in Arnimallee 3. You can also hand them in at the beginning of the tutorial.
• The exercises consist of theoretical problems as well as numerical experiments. Both types of exercises are rated seperately by an appropiate number of either theory points (TP) or programing points (PP). Numerical experiments have to be handled using Matlab (available at the students computer pool at the institute). A complete solution for a numerical experiment consists of a running Matlab code, a program executing the required test runs and protocols of the execution of these test runs. Please deliver your programs by e-mail as well as printed out to the tutor. Don't forget to mention all team members in your e-mails and programs.
• Caution: Delivering a correct and running code without knowing what's going on in the code will be regarded and rated as attempt of deception.

Klausur

• There will be a Klausur at the end of the semester. All students inscribed at KVV for this course are allowed to participate.
• Students who fail in the Klausur have a second chance in the Nachklausur.

Criteria for the Certificate (Übungsschein)

Neccessary and sufficient for a certificate are:

• passing the Klausur or the Nachklausur
• active participation (50% of all theory points and 50% of all programing points)
• constant participation (85% presence in the tutorial) (suspended since November 1, 2010)

Certificates are graded according to the result of the Klausur.

Exercises

• Exercise 1
• Exercise 2
• Exercise 3
• Exercise 4
• Exercise 5
• Exercise 6
• Exercise 7
• Exercise 8, basis.m, quadrature.m
• Exercise 9, uniform_grid.m, generate_grid.m, circle.mat, assemble_mass.m, assemble_stiff.m
• Exercise 10, hierarchic_basis.m, refine_grid.m, assemble_P1.m
• Exercise 11

Accompanying Material

Lecture Notes:

The lecture notes are available here (in German only).

Here are the lecture notes for previous courses Numerics I, in German only, and Numerics II.

Matlab:

Here you can find an introduction to Matlab (in german only).

Literature

The following selection of textbooks can be found in the in the reserved books section (Handapparat) on numerical mathematics in the institutes library (Arnimallee 3) opposite to the reception and to the left of the door to the journals section.

1. F. John: Partial Differential Equations. Springer (1982)
2. M. Renardy, R. C. Rogers: An introduction to partial differential equations, Springer, 2. Auflage (2004)
3. P. Deuflhard, M. Weiser: Numerische Mathematik 3: Adaptive Lösung partieller Differentialgleichungen. de Gruyter. (2011)
4. A. Quarteroni, R. Sacco, F. Saleri: Numerische Mathematik 2. Springer (2002)
5. D. Braess: Finite Elemente. Springer, 3. Auflage (2002)
6. P. A. Raviart, J. M. Thomas: Introduction à l'analyse numérique des équations aux dérivées partielles, Dunod (1998)

Further literature on numerics is deposited under the shelf marks H.1.0 and H.1.1.

Introductory literature in computer science can be found under XA.1, introductions in Unix operating system under XD.4.0.

Contact