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SUMMARY:Discrete De Giorgi-Nash-Moser Theory: Analysis and Applications - 
 Endre Suli (Oxford)
DTSTART:20230511T140000Z
DTEND:20230511T150000Z
UID:TALK198046@talks.cam.ac.uk
CONTACT:Matthew Colbrook
DESCRIPTION:The talk is concerned with a class of numerical methods for th
 e approximate solution of a system of nonlinear elliptic partial different
 ial equations that arise in models of chemically-reacting viscous incompre
 ssible non-Newtonian fluids. In order to prove the convergence of the nume
 rical method under consideration one needs to derive a uniform Hölder nor
 m bound on the sequence of approximations in a setting where the diffusion
  coefficient in the convection-diffusion equation involved in the system i
 s merely a bounded function with no additional regularity. This necessitat
 es the development of a discrete counterpart of De Giorgi’s elliptic reg
 ularity theory\, which is then used\, in combination with various weak com
 pactness techniques\, to deduce the convergence of the sequence of numeric
 al solutions to a weak solution of the system of partial differential equa
 tions. The theoretical result are illustrated by numerical experiments for
  a model of the synovial fluid\, a non-Newtonian chemically-reacting incom
 pressible fluid contained in the cavities of human joints.
LOCATION:Centre for Mathematical Sciences\, MR14
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