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UID:7858@test.i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20230121T160000
DTEND;TZID=Europe/Paris:20230121T170000
DTSTAMP:20221118T174636Z
URL:https://test.i2m.univ-amu.fr/events/introduction-to-the-discrete-de-rh
am-complex/
SUMMARY:Introduction to the Discrete De Rham complex - Jérôme Droniou
DESCRIPTION:Hilbert complexes are chains of spaces linked by operators\, wi
th properties that are crucial to establish the well-posedness of certain
systems of partial differential equations.\nDesigning stable numerical sch
emes for such systems\, without resorting to non-physical stabilisation pr
ocesses\, requires reproducing the complex properties at the discrete leve
l.\nFinite-element complexes have been extensively developed since the lat
e 2000's\, in particular by Arnold\, Falk\, Winther and collaborators. The
se are however limited to certain types of meshes (mostly\, tetrahedral an
d hexahedral meshes)\, which limits options for\, e.g.\, local mesh refine
ment.\nIn this talk we will introduce the Discrete De Rham complex\, a dis
crete version of one of the most popular complexes of differential operato
rs (involving the gradient\, curl and divergence)\, that can be applied on
meshes made of generic polytopes.\nWe will use the Stokes problem in curl
-curl formulation to motivate the need for (continuous and discrete) compl
exes\, then give a presentation\nof the lowest-order version of the comple
x. We will then briefly explain how this lowest-order version is naturally
extended to an arbitrary-order version\, and present the associated pro
perties (Poincaré inequalities\, primal and adjoint consistency\, commuta
tion properties\, etc.) that enable the analysis of schemes based on this
complex. For the Stokes problem we will see that using this complex leads
to a pressure-robust scheme.
ATTACH;FMTTYPE=image/jpeg:https://test.i2m.univ-amu.fr/wp-content/uploads/
2020/03/Jerome_Droniou.jpg
CATEGORIES:GdT HYPERBO,Séminaire Analyse Appliquée (AA)
LOCATION:FRUMAM\, St Charles (2ème étage)\, 3 Place Victor Hugo\, Marseil
le\, 13003\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse
ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=FRUMAM\, St Charles (2èm
e étage):geo:0,0
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DTSTART:20221030T020000
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