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| ICM | IWR |
| IGK-Heidelberg | |
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Contact 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 |
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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. |