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SUMMARY:Finite element exterior calculus - 4 - Douglas Arnold (University 
 of Minnesota)
DTSTART:20190712T130000Z
DTEND:20190712T140000Z
UID:TALK127225@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:These lectures aim to provide an introduction and overview of 
 Finite Element Exterior Calculus\, a transformative approach to designing 
 and understanding numerical methods for partial differential equations.  T
 he first lecture will introduce some of the key tools--chain complexes and
  their cohomology\, closed operators in Hilbert space\, and their marriage
  in the notion of Hilbert complexes--and explore their application to PDEs
 .  The lectures will continue with a study of the properties needed to eff
 ectively discretize Hilbert complexes\, illustrating the abstract framewor
 k on the concrete example of the de Rham complex and its applications to p
 roblems such as Maxwell&#39\;s equation.  The third lecture will get into 
 differential forms and their discretization by finite elements\, bringing 
 in new tools like the Koszul complex and bounded cochain projections and r
 evealing the Periodic Table of Finite Elements.  Finally in the final lect
 ure we will examine new complexes\, their discretization\, and application
 s.
LOCATION:Seminar Room 1\, Newton Institute
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