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CATEGORIES:Applied and Computational Analysis
SUMMARY:Finite Element Exterior Calculus for Hamiltonian P
DEs - Ari Stern (Washington University in St. Loui
s)
DTSTART;TZID=Europe/London:20240613T150000
DTEND;TZID=Europe/London:20240613T160000
UID:TALK217189AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/217189
DESCRIPTION:We consider the application of finite element exte
rior calculus (FEEC) methods to a class of canonic
al Hamiltonian PDE systems involving differential
forms. Solutions to these systems satisfy a local
multisymplectic conservation law\, which generaliz
es the more familiar symplectic conservation law f
or Hamiltonian systems of ODEs\, and which is conn
ected with physically-important reciprocity phenom
ena\, such as Lorentz reciprocity in electromagnet
ics. We characterize hybrid FEEC methods whose num
erical traces satisfy a version of the multisymple
ctic conservation law\, and we apply this characte
rization to several specific classes of FEEC metho
ds\, including conforming Arnold–Falk–Winther-type
methods and various hybridizable discontinuous Ga
lerkin (HDG) methods. Interestingly\, the HDG-type
and other nonconforming methods are shown\, in ge
neral\, to be multisymplectic in a stronger sense
than the conforming FEEC methods. This substantial
ly generalizes previous work of McLachlan and Ster
n [Found. Comput. Math.\, 20 (2020)\, pp. 35–69] o
n the more restricted class of canonical Hamiltoni
an PDEs in the de Donder–Weyl grad-div form.
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Matthew Colbrook
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