Theory and Numerics for Partial Differential Equations – Selected Nonlinear Problems

Time/Place: Monday 12 a.m. to 2 p.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 Tatjana Schreiber
Office hour: at any time by appointment, Room 211, Hermann-Herder-Str. 10
E-Mail: tatjana.stiefken@mathematik.uni-freiburg.de

Contents

The lecture covers nonlinear partial differential equations both analytically and numerically. The focus is on minimization problems, in particular harmonic maps, total variation, and the p-Laplace problem. The analytical treatment of the problems uses methods from variational calculus. The numerical approximation uses finite element methods. The lecture is accompanied by a practical course in which the implementation of selected problems is discussed.

Studienleistung/Prüfungsleistung

Studienleistung lecture:
  • 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 lecture:
  • Pass the exam at the end of the semester.
Studienleistung practical Exercises:
  • 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.
Zeitraum Inhalte Erklärvideos Skript
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Exercises

Hand in your solutions to the letterbox on the second floor of the Rechenzentrum (mailbox 8). You can submit your solutions in teams of two.

Exercise groups

The tutorial starts in the second week of lectures.

Group Tutor Time/Place
1 Dominik Schneider (dominik.schneider@mathematik.uni-freiburg.de) and Tatjana Schreiber (tatjana.stiefken@mathematik.uni-freiburg.de) tba

Practical Exercices

Please send your solutions to the tutor Stefan Kater (stefan.kater@mathematik.uni-freiburg.de ).

Exercise Groups

The practice groups will meet every two weeks starting on October 28, always on tba, in person at the CIP pool.

Literatur

  1. S.Bartels: Numerical Approximation of Partial Differential Equations, Springer, 2016
  2. S. Bartels: Numerical Methods for Nonlinear Partial Differential Equations, Springer, 2015
  3. B. Dacorogna: Direct Methods in the Calculus of Variations (Second Edition), Springer, 2008.

You can download the books free of charge if you are connected to the university network.