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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Finite Element Exterior Calculus - 1 - Douglas Arn
old (University of Minnesota)
DTSTART;TZID=Europe/London:20190709T090000
DTEND;TZID=Europe/London:20190709T100000
UID:TALK127021AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/127021
DESCRIPTION:These lectures aim to provide an introduction and
overview of Finite Element Exterior Calculus\, a t
ransformative approach to designing and understand
ing numerical methods for partial differential equ
ations. The first lecture will introduce some of
the key tools--chain complexes and their cohomolog
y\, closed operators in Hilbert space\, and their
marriage in the notion of Hilbert complexes--and e
xplore their application to PDEs. The lectures wi
ll continue with a study of the properties needed
to effectively discretize Hilbert complexes\, illu
strating the abstract framework on the concrete ex
ample of the de Rham complex and its applications
to problems such as Maxwell'\;s equation. The
third lecture will get into differential forms and
their discretization by finite elements\, bringin
g in new tools like the Koszul complex and bounded
cochain projections and revealing the Periodic Ta
ble of Finite Elements. Finally in the final lect
ure we will examine new complexes\, their discreti
zation\, and applications.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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