BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Finite Element Exterior Calculus for Hamiltonian PDEs - Ari Stern 
 (Washington University in St. Louis)
DTSTART:20240613T140000Z
DTEND:20240613T150000Z
UID:TALK217189@talks.cam.ac.uk
CONTACT:Matthew Colbrook
DESCRIPTION:We consider the application of finite element exterior calculu
 s (FEEC) methods to a class of canonical Hamiltonian PDE systems involving
  differential forms. Solutions to these systems satisfy a local multisympl
 ectic conservation law\, which generalizes the more familiar symplectic co
 nservation law for Hamiltonian systems of ODEs\, and which is connected wi
 th physically-important reciprocity phenomena\, such as Lorentz reciprocit
 y in electromagnetics. We characterize hybrid FEEC methods whose numerical
  traces satisfy a version of the multisymplectic conservation law\, and we
  apply this characterization to several specific classes of FEEC methods\,
  including conforming Arnold–Falk–Winther-type methods and various hyb
 ridizable discontinuous Galerkin (HDG) methods. Interestingly\, the HDG-ty
 pe and other nonconforming methods are shown\, in general\, to be multisym
 plectic in a stronger sense than the conforming FEEC methods. This substan
 tially generalizes previous work of McLachlan and Stern [Found. Comput. Ma
 th.\, 20 (2020)\, pp. 35–69] on the more restricted class of canonical H
 amiltonian PDEs in the de Donder–Weyl grad-div form.
LOCATION:Centre for Mathematical Sciences\, MR14
END:VEVENT
END:VCALENDAR