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SUMMARY:Andreas Rupp (Lappeenranta-Lahti University of Technology)
DTSTART:20240219T121500Z
DTEND:20240219T130000Z
DTSTAMP:20260417T004543Z
UID:cam/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/cam/18/">Par
 tial differential equations on hypergraphs and networks of surfaces</a>\nb
 y Andreas Rupp (Lappeenranta-Lahti University of Technology) as part of CA
 M seminar\n\nLecture held in MV:L14.\n\nAbstract\nAlbeit many physical\, s
 ociological\, engineering\, and economic processes have been described by 
 partial differential equations posed on domains which cannot be described 
 as subsets of linear spaces or smooth manifolds\, there is still a lack of
  mathematical tools and general purpose software specifically addressing t
 he challenges arising from the discretization of these models.\n\nThis pre
 sentation establishes a general approach to formulate partial differential
  equations (PDEs) on networks of (hyper)surfaces\, referred to as hypergra
 phs. Such PDEs consist of differential expressions with respect to all hyp
 eredges (surfaces) and compatibility conditions on the hypernodes (joints\
 , intersections of surfaces). These compatibility conditions ensure conser
 vation properties (in case of continuity equations) or incorporate other p
 roperties – motivated by physical or mathematical modeling. We illuminat
 e how to discretize such equations numerically using hybrid discontinuous 
 Galerkin (HDG) methods. These methods consist of local solvers (encoding t
 he differential expressions on hyperedges) and a global compatibility cond
 ition (related to our hypernode conditions). We complement the physically 
 motivated compatibility conditions by a derivation through a singular limi
 t analysis of thinning structures yielding the same results.\n
LOCATION:https://researchseminars.org/talk/cam/18/
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