Numerik IV

News and Important Remarks


Lecture Tue, 8:00 - 10:00 Arnimallee 3, SR 119
Tutorial Wed, 14:00 - 16:00 Takustraße 9, SR 051
Oral Exam Thu, 14.2.2013 and Fr, 15.2.2013 Arnimalle 6, Room 130

General Information


Geometric partial differential equations are describing the evolution of and processes on surfaces. Geometric flows such as the now classical mean curvature flow, Willmore flow, and pdes on moving surfaces are typical examples. In this lecture, we will consider various formulations including phase field models of Allen-Cahn and Cahn-Hilliard type and concentrate on basic numerical techniques such as surface finite element methods, adaptivity, unfitted finite element methods, and efficient numerical solvers.

Target Audience

Advanced students in the Master Program Mathematics. Various possible topics for a Master thesis will come up during this course.


Basic knowledge on partial differential equations and their numerical solution (e.g. Numerik III).


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 oral exams. 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:

Exercises and Criteria for a Certificate

Tutorial & Exercises

Oral Exam

Criteria for the Certificate (Übungsschein)

Neccessary and sufficient for a certificate are:

Certificates are graded according to the result of the oral exam.


Accompanying Material

Here you can find an Introduction to Viscosity Solutions

Lecture Notes:

Here are the lecture notes for previous course Numerics III


  1. M. Brokate and J. Sprekels: Hysteresis and Phase Transitions. Springer (1996)
  2. K. Deckelnick, G. Dziuk, and Ch.M. Elliott: Computation of geometric partial differential equations and mean curvature flow. Acta Numerica, p. 1-94 (2005)
  3. G. Dziuk and Ch.M. Elliott: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, p. 262-292 (2007)
  4. J.A. Sethian: Level Set Methods and Fast Marching Methods, Cambridge University Press (1999)
  5. T.J. Willmore: Riemannian Geometry, Clarendon, Oxford (1993)


Prof. Dr. Ralf Kornhuber Arnimalle 6, Room 130
Secretary Frau Nordt: Arnimallee 6, Room 131
Consultation: Thu, 11:00-12:00
email: kornhube{at}
Maren-Wanda Wolf Arnimalle 6, Room 122
Consultation: Wed, 11:00-12:00
email: mawolf{at}