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SUMMARY:Optimal error bounds in stochastic homogenization - Otto\, F (Bonn
 )
DTSTART:20100330T090000Z
DTEND:20100330T100000Z
UID:TALK23974@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We consider one of the simplest set-ups in stochastic homogeni
 zation:\nA discrete elliptic differential equation on a d-dimensional latt
 ice with identically independently distributed bond conductivities. It is 
 well-known that on scales large w. r. t. the grid size\, the resolvent ope
 rator behaves like that of a homogeneous\, deterministic (and\ncontinuous)
  elliptic equation. The homogenized coefficients can be characterized by a
 n ensemble average with help of the corrector problem. For a numerical tre
 atment\, this formula has to be approximated in two ways: The corrector pr
 oblem has to be solved on a finite sublattice (with\, say\, periodic bound
 ary conditions) and the ensemble average has to be replaced by a spatial a
 verage. We give estimates on both errors that are optimal in terms of the 
 scaling in the size of the sublattice. This is joint work with Antoine Glo
 ria (INRIA Lille).
LOCATION:Seminar Room 1\, Newton Institute
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