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SUMMARY:Felix Otto (Max Planck Institute for Mathematics in the Sciences\,
  Leipzig\, Germany)
DTSTART:20200903T153000Z
DTEND:20200903T163000Z
DTSTAMP:20260423T040043Z
UID:SIAM-PDE/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SIAM-PDE/3/"
 >The thresholding scheme for mean curvature flow and De Giorgi's ideas for
  gradient flows</a>\nby Felix Otto (Max Planck Institute for Mathematics i
 n the Sciences\, Leipzig\, Germany) as part of Seminar In the Analysis and
  Methods of PDE (SIAM PDE)\n\n\nAbstract\nFlow of interfaces by mean curva
 ture\, in its multi-phase version\,\nwas first formulated in the context o
 f grain growth in polycrystalline materials. \nThe computationally efficie
 nt and very popular thresholding scheme\nfor mean curvature flow by Osher 
 et. al. can be naturally extended \nto such a multi-phase situation\, even
  for surface tensions that depend on \nthe lattice mismatch between the ad
 jacent grains.\n\nThis extension relies on the gradient flow structure of 
 mean curvature flow\,\nand the interpretation of the thresholding scheme\n
 as a corresponding "minimizing movements'' scheme\, that is\, a sequence o
 f variational problems\nnaturally attached to the implicit time discretiza
 tion of a gradient flow.\n\nThis interpretation also allows for a (conditi
 onal) convergence proof based on De Giorgi's ideas\nfor gradient flows in 
 metric spaces. The approach is similar to\nthe convergence proof for the m
 inimizing movement scheme by Almgren\, Taylor and Wang\,\nas given by Luck
 haus et. al. \n\nThis is joint work with S. Esedoglu and T. Laux.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/3/
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