Introduction to Theory and Numerics of Partial Differential Equations

Time/Place: Tue & Thu 10-12 a.m., SR 226, Hermann-Herder-Str. 10
Lecturer: Prof. Dr. Sören Bartels
Office hour: Tue 12-1 p.m., Room 209, Hermann-Herder-Str. 10
Exercises & Practical Course Vera Jackisch
Office hour: at any time by appointment, Room 207, Hermann-Herder-Str. 10
E-Mail: vera.jackisch@mathematik.uni-freiburg.de

News

  • Since Friday, 1.11., is a holiday, the tutorial group will instead take place on Wednesday, 30.10., 2-4 p.m. (same room).
  • Please register for the lecture, the exercise group and the practical course on HisinOne during the first week of lectures.

Contents

The aim of this course is to give an introduction into theory of linear partial differential equations and their finite difference as well as finite element approximations. Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensable tool in science and technology. We provide an introduction to the construction, analysis, and implementation of finite element methods for different model problems. We will address elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods.

In the practical course, the algorithms presented in the lecture are implemented and tested in practice. The commercial software MATLAB (see below for a guide to obtain a licence through the university) will be used to solve and visualize mathematical problems. Elementary programming skills are required.

Necessary Prerequisites

Analysis I and II, Linear Algebra I and II und knowledge about higher-dimensional integration (e.g. from Analysis III or “Erweiterung der Analysis”)
Useful, but not necessary: Numerics for differential equations, functional analysis

Studienleistung/Prüfungsleistung

Studienleistung Vorlesung:
  • Obtain at least 50% of possible points in the exercise sheets overall.
  • At least one presentation of an exercise on the blackboard during the exercise group. Any request to do so by the tutor must be complied with.
Prüfungsleistung Vorlesung:
  • Pass the exam at the end of the semester.
Studienleistung Praktikum:
  • Obtain at least 50% of possible points in the exercise sheets overall
  • You should be able to explain your code upon request during the practical course.

Important Dates

What When Where
Register for exercise group first week of lectures online (HisinOne)

Exercises

Hand in your solutions to the letterbox on the second floor of the Rechenzentrum. You can submit your solutions in teams of two.

Exercise Sheet Start Date Submission Date
Sheet 1 15.10.2024 22.10.2024, 10 a.m.
Sheet 2 22.10.2024 29.10.2024, 10 a.m.
Sheet 3 29.10.2024 05.11.2024, 10 a.m.
Sheet 4 05.11.2024 12.11.2024, 10 a.m.
Sheet 5 12.11.2024 19.11.2024, 10 a.m.
Sheet 6 19.11.2024 26.11.2024, 10 a.m.
Sheet 7 26.11.2024 03.12.2024, 10 a.m.
Sheet 8 03.12.2024 10.12.2024, 10 a.m.
Sheet 9 10.12.2024 17.12.2024, 10 a.m.
Blatt 10 17.12.2024 07.01.2025, 10 a.m.

Practical course exercises

Hand in your solutions via E-Mail to the tutor with your source code attached.
Project 1 - 3: dominik.schneider@mathematik.uni-freiburg.de
Project 4 - 6: stefan.kater@mathematik.uni-freiburg.de

Project Start Date Submission Date
Project 1 23.10.2024 06.11.24, 9 a.m.
Project 2 06.11.2024 20.11.2024, 9 a.m.
Project 3 20.11.2024 04.12.2024, 9 a.m.
Projekt 4 04.12.2024 18.12.2024, 9 a.m.
Projekt 5 18.12.2024 08.01.2025, 9 a.m.

Exercise groups

The tutorial starts in the second week of lectures.

Group Tutor Time/Place
1 Michael Fr 8-10 a.m., SR 125/126 (Ernst-Zermelo-Str. 1)

Practical Course

The practical course starts in the second week of lectures and consists of one tutorial session every two weeks and an office hour in the week in between.

Group Tutor Time/Place
1 Dominik/Stefan Wed 10-12, CIP-Pool (Hermann-Herder-Str. 10)
Office hours take place Wed 10-11, Hermann-Herder-Str. 10, Room 210 (Dominik) and Room 228 (Stefan).

Literature

Software