The Graduate College "Complex processes: Modelling, Simulation and Optimization"
ICM IWR
IGK-Heidelberg
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Graduate College
ICM
Pawinskiego 5a
02-106 Warsaw

e-mail: gradkol@icm.edu.pl
fax: +48 22 8749115
 


Prof. Gerhard Dziuk
Numerical methods for transient geometric partial differential equations
The main geometric flow problems are gradient flows for geometric energies. Mean curvature flow is the gradient flow for area, Willmore flow appears as gradient flow of the Willmore functional, i. e. the classical bending energy. Besides their mathematical beauty these flows are of interest for a wide range of applications such as phase transition problems and image processing.

These geometric flows lead to highly nonlinear parabolic and degenerate partial differential equations of second and fourth order. We give a survey over the discretization by finite elements and discuss stability and convergence of the algorithms.
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