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SUMMARY:A few elements of numerical analysis for PDEs with random coeffici
 ents of lognormal type - Julia  Charrier  (Aix Marseille Université)
DTSTART:20180110T090000Z
DTEND:20180110T100000Z
UID:TALK97498@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this talk\, we will address some basic issues appearing in 
 the theoretical analysis of numerical methods for PDEs with random coeffic
 ients of lognormal type. To begin with\, such problems will be motivated b
 y applications to the study of subsurface flow with uncertainty. We will t
 hen give some results concerning the spatial regularity of solutions of su
 ch problems\, which of course impacts the error committed in spatial discr
 etization. We will complete these results with integrability properties to
  deal with unboundedness of these solutions and then give error bounds for
  the finite element approximations in adequate norms.  Finally we will dis
 cuss the question of the dimensionality\, which is crucial for numerical m
 ethods such as stochastic collocation. We will consider the approximation 
 of the random coefficient through a Karhunen-Lo&egrave\;ve expansion\, and
  provide bounds of the resulting error on the solution by highlighting the
  interest of the notion of weak error.
LOCATION:Seminar Room 1\, Newton Institute
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