Numerics III

News

• The results of the second exam can be found here.
• The results of the first exam can be found here.
• The first tutorial is on Tue 2018-04-24, 10:15.
• The first lecture is on Mon 2018-04-16, 12:15.

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 Bachelor and Master courses in Mathematics and of BMS.

Prerequisites

Basic knowledge in calculus (Analysis I-III) and Numerical Analysis (Numerik I). Some knowledge in Functional Analysis will help but is not necessary.

Registration

All participants should register at the KVV, so that we know who is participating. The overall number of participants is also necessary to justify the equipment of the course. In addition, depending on your program of study, you have to register in the Campus Management.

Exercises and Criteria for a Certificate

Tutorial & Exercises

• The tutorial offers the possibility to discuss and better understand the presented material and exercises. Furthermore solutions of exercises are presented by the students.
• Each week a sheet with exercises will be made available electronically on this web page (see below).
• The exercises are intended to be solved by teams .
• The exercises consist of theoretical and numerical problems that should be solved by the teams.
• Programming exercises should be solved using Matlab (available at the students computer pool at the institute). Both types of exercises are rated separately.
• The solutions have to be finished before the tutorial two weeks after they were handed out.
• The solutions of the numerical problems should be delivered by email to adjurdjevac@math.fu-berlin.de. Note that 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. Delivering a correct and running code without knowing what is going on in the code will be regarded and rated as attempt of deception.

Exam

• There will be an exam at the end of the semester.

Criteria for the Certificate

Necessary and sufficient for a certificate are:

• exam: passing the exam
• active participation: presentation of solutions in the tutorial, at least 60 % of both, theoretical and programming points.
• regular participation: regular attedence in the tutorial

Certificates are graded according to the result of the exam.

Exercises

• Exercise 1

• Exercise 2

• Exercise 3

• Exercise 4

• Exercise 5

• Exercise 6

• Exercise 7

• Exercise 8

• Exercise 9 (provided sources: basis.m, quadrature.m, uniform_grid.m, generate_grid.m, circle.mat, assemble_mass.m, assemble_stiff.m)

  Accompanying Material

  Lecture Notes

  The lecture notes are available here.

  Matlab

  Here you can find an introduction to Matlab (in German, sorry).

  Literature

  • D. Braess: Finite Elemente. Springer, 3rd edition (2002)
  • P. Knabner, L. Angermann: Numerik partieller Differentialgleichungen. Springer (2000)
  • P. Deuflhard, M. Weiser: Numerische Mathematik 3. De Gruyter (2011)
  • J. Wloka: Partielle Differentialgleichungen. Teubner (1982)
  • D. Werner: Funktionalanalysis. Springer, Berlin (2000)
  • H. Alt: Lineare Funktionalanalysis. Sprinter, 6th edition (2012)
  • W. Rudin: Functional Analysis. McGraw-Hill, 2nd edition (1991)
  • L. Evans: Partial Differential Equations. AMS, 19th volume (1998)
  • F. John: Partial Differential Equations. Springer (1982)
  • M. Renardy, R. C. Rogers: An introduction to partial differential equations. Springer, 2nd volume (2004)
  • A. Quarteroni, R. Sacco, F. Saleri: Numerische Mathematik 2. Springer (2002)
  • P. A. Raviart, J. M. Thomas: Introduction à l'analyse numérique des équations aux dérivées partielles. Dunod (1998)

  Contact

  Prof. Dr. Carsten Gräser	graeser@mi.fu-berlin.de	Arnimallee 6, Room 121 consultation-hour: Mon 14:00-15:00
  Ana Djurdjevac (Assistentin)	adjurdjevac@math.fu-berlin.de	Arnimallee 6, Raum 120 consultation-hour: Thur 12:00-13:00