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UID:5782@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20230121T160000
DTEND;TZID=Europe/Paris:20230121T170000
DTSTAMP:20241120T200216Z
URL:https://www.i2m.univ-amu.fr/evenements/introduction-to-the-discrete-de
 -rham-complex/
SUMMARY:Jérôme Droniou (Monash university (Melbourne\, Australia)): Intro
 duction to the Discrete De Rham complex
DESCRIPTION:Jérôme Droniou: Hilbert complexes are chains of spaces linked
  by operators\, with properties that are crucial to establish the well-pos
 edness of certain systems of partial differential equations.\nDesigning st
 able numerical schemes for such systems\, without resorting to non-physica
 l stabilisation processes\, requires reproducing the complex properties at
  the discrete level.\nFinite-element complexes have been extensively devel
 oped since the late 2000's\, in particular by Arnold\, Falk\, Winther and 
 collaborators. These are however limited to certain types of meshes (mostl
 y\, tetrahedral and hexahedral meshes)\, which limits options for\, e.g.\,
  local mesh refinement.\nIn this talk we will introduce the Discrete De Rh
 am complex\, a discrete version of one of the most popular complexes of di
 fferential operators (involving the gradient\, curl and divergence)\, that
  can be applied on meshes made of generic polytopes.\nWe will use the Stok
 es problem in curl-curl formulation to motivate the need for (continuous a
 nd discrete) complexes\, then give a presentation\nof the lowest-order ver
 sion of the complex. We will then briefly explain how this lowest-order ve
 rsion is naturally extended to an arbitrary-order version\,  and present 
 the associated properties (Poincaré inequalities\, primal and adjoint con
 sistency\, commutation properties\, etc.) that enable the analysis of sche
 mes based on this complex. For the Stokes problem we will see that using t
 his complex leads to a pressure-robust scheme.
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/03/Jerome_Droniou.jpg
CATEGORIES:Groupe de travail,Séminaire,Analyse Appliquée,HYPERBO
LOCATION:Saint-Charles - FRUMAM  (2ème étage)\, 3 Place Victor Hugo\, Mar
 seille\, 13003\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse
 ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=Saint-Charles - FRUMAM  (
 2ème étage):geo:0,0
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DTSTART:20221030T020000
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