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UID:5187@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20240618T110000
DTEND;TZID=Europe/Paris:20240618T120000
DTSTAMP:20241130T124805Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-46-2/
SUMMARY:Bouchra Bensiali (École Centrale Casablanca (Maroc)): Boundary lay
 er analysis of a d-dimensional penalization method for Neumann or Robin bo
 undary conditions
DESCRIPTION:Bouchra Bensiali: A d-dimensional extension of a fictitious dom
 ain penalization technique that we previously proposed for Neumann or Robi
 n boundary conditions will be presented. We apply Droniou's approach for n
 on-coercive linear elliptic problems to obtain the existence and uniquenes
 s of the solution of the penalized problem\, and we derive a boundary laye
 r approach to establish the convergence of the penalization method. The de
 veloped boundary layer approach is adapted from the one used for Dirichlet
  boundary conditions\, but in contrast to the latter where coercivity enab
 les a straightforward estimate of the remainders\, we reduce the convergen
 ce of the penalization method to the existence of suitable supersolutions 
 of a dual problem. These supersolutions are then constructed as approximat
 e solutions of the dual problem using an additional formal boundary layer 
 approach.\n\nThe proposed approach results in an advection-dominated probl
 em\, requiring the use of appropriate numerical methods suitable for singu
 lar perturbation problems\, such as upwind finite differences or stabilize
 d finite elements. Numerical experiments validate both the convergence rat
 e and the boundary layer thickness\, illuminating the theoretical results.
 \n\nFinally\, we investigate the applicability of the suggested method to 
 the simulation of population dynamics under climate change. The fact that 
 climate change causes the climate envelope to shift over time motivates th
 e idea of using a penalization method to prevent the need for costly remes
 hing of the spatial domain at each time step.\n\nThis talk comprises joint
  work with Jacques Liandrat\, Centrale Méditerranée\, I2M.
CATEGORIES:Séminaire,Analyse Appliquée
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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