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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Optimal error bounds in stochastic homogenization
- Otto\, F (Bonn)
DTSTART;TZID=Europe/London:20100330T100000
DTEND;TZID=Europe/London:20100330T110000
UID:TALK23974AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/23974
DESCRIPTION:We consider one of the simplest set-ups in stochas
tic homogenization:\nA discrete elliptic different
ial equation on a d-dimensional lattice with ident
ically independently distributed bond conductiviti
es. It is well-known that on scales large w. r. t.
the grid size\, the resolvent operator behaves li
ke that of a homogeneous\, deterministic (and\ncon
tinuous) elliptic equation. The homogenized coeffi
cients can be characterized by an ensemble average
with help of the corrector problem. For a numeric
al treatment\, this formula has to be approximated
in two ways: The corrector problem has to be solv
ed on a finite sublattice (with\, say\, periodic b
oundary conditions) and the ensemble average has t
o be replaced by a spatial average. We give estima
tes on both errors that are optimal in terms of th
e scaling in the size of the sublattice. This is j
oint work with Antoine Gloria (INRIA Lille).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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