Numerics III

News

Dates

Lecture Mon, 10-12h WebEx Prof. Dr. Ralf Kornhuber
Mon, 14-16h WebEx
Tutorial Fr, 10-12h WebEx Xingjian Zhang-Schneider
Exam July 6,7 TBA
Second exam October 26 TBA

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

Individual Exam

Criteria for the Certificate

Necessary and sufficient for a certificate are:

The grade of final certificate is the grade of the individual exam.

Exercises

Lecture Notes

The lecture notes are available here.

Accompanying Material

Jinchao Xu, Iterative methods by space decomposition and subspace correction

Harry Yserentant, Old and New Convergence Proofs for Multigrid Methods

A short survey about the Dirichlet Problem can be found here.

Notes from June 22 can be found here.

A survey about hierarchical error estimates can be found here.

Matlab

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

Literature

Contact

Prof. Dr. Ralf Kornhuber ralf.kornhuber@fu-berlin.de Arnimallee 6, Room 130
open
Xingjian Zhang-Schneider (Assistent) xingjian@zedat.fu-berlin.de Arnimallee 9, Raum 125