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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Approximation of Harmonic Maps and Wave Maps - Soe
ren Bartels (Albert-Ludwigs-Universität Freiburg)
DTSTART;TZID=Europe/London:20191002T110000
DTEND;TZID=Europe/London:20191002T120000
UID:TALK130660AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/130660
DESCRIPTION:Partial differential equations with a nonlinear po
intwise constraint defined by a manifold occur in
a variety of applications: the magnetization of a
ferromagnet can be described by a unit length vect
or field and the orientation of the rod-like molec
ules that constitute a liquid crystal is often mod
eled by a restricted vector field. Other applicati
ons arise in geometric modeling\, nonlinear bendin
g of solids\, and quantum mechanics. Nodal finite
element methods have to appropriately relax the po
intwise constraint leading to a variational crime.
Since exact solutions are typically nonunique and
do not admit higher regularity properties\, the c
orrectness of discretizations has to be establishe
d by weaker means avoiding unrealistic conditions.
The iterative solution of the nonlinear systems o
f equations can be based on linearizations of the
constraint or by using appropriate constraint-pres
erving reformulations. The talk focusses on the ap
proximation of harmonic maps and wave maps. The la
tter arise as a model problem in general relativit
y.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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