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SUMMARY:FEEC 4 GR? - Douglas Arnold (University of Minnesota)
DTSTART:20191003T150000Z
DTEND:20191003T160000Z
UID:TALK130819@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The finite element exterior calculus (FEEC) has proven to be a
  powerful tool for the design and understanding of numerical methods for s
 olving PDEs from many branches of physics: solid mechanics\, fluid flow\, 
 electromagnetics\, etc.  Based on preserving crucial geometric and topolog
 ical structures underlying the equations\, it is a prime example of a stru
 cture-preserving numerical method.  It has organized many known finite ele
 ment methods resulting in the periodic table of finite elements.  For elas
 ticity\, which is not covered by the table\, it led to new methods with lo
 ng sought-after properties.  Might the FEEC approach lead to better numeri
 cal solutions of the Einstein equations as well?  This talk will explore t
 his question through two examples: the Einstein--Bianchi formulation of th
 e Einstein equations based on Bel decomposition of the Weyl tensor\, and t
 he Regge elements\, a family of finite elements inspired by Regge calculus
 .  Our goal in the talk is to raise questions and inspire future work\; we
  do not purport to provide anything near definitive answers.<br>
LOCATION:Seminar Room 1\, Newton Institute
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