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SUMMARY:Approximation of Harmonic Maps and Wave Maps - Soeren Bartels (Alb
 ert-Ludwigs-Universität Freiburg)
DTSTART:20191002T100000Z
DTEND:20191002T110000Z
UID:TALK130657@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Partial differential equations with a nonlinear pointwise cons
 traint defined by a manifold occur in a variety of applications: the magne
 tization of a ferromagnet can be described by a unit length vector field a
 nd the orientation of the rod-like molecules that constitute a liquid crys
 tal is often modeled by a restricted vector field. Other applications aris
 e in geometric modeling\, nonlinear bending of solids\, and quantum mechan
 ics. Nodal finite element methods have to appropriately relax the pointwis
 e constraint leading to a variational crime. Since exact solutions are typ
 ically nonunique and do not admit higher regularity properties\, the corre
 ctness of discretizations has to be established by weaker means avoiding u
 nrealistic conditions. The iterative solution of the nonlinear systems of 
 equations can be based on linearizations of the constraint or by using app
 ropriate constraint-preserving reformulations. The talk focusses on the ap
 proximation of harmonic maps and wave maps. The latter arise as a model pr
 oblem in general relativity.
LOCATION:Seminar Room 1\, Newton Institute
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