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CATEGORIES:Applied and Computational Analysis
SUMMARY:Discrete De Giorgi-Nash-Moser Theory: Analysis and
Applications - Endre Suli (Oxford)
DTSTART;TZID=Europe/London:20230511T150000
DTEND;TZID=Europe/London:20230511T160000
UID:TALK198046AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198046
DESCRIPTION:The talk is concerned with a class of numerical me
thods for the approximate solution of a system of
nonlinear elliptic partial differential equations
that arise in models of chemically-reacting viscou
s incompressible non-Newtonian fluids. In order to
prove the convergence of the numerical method und
er consideration one needs to derive a uniform Höl
der norm bound on the sequence of approximations i
n a setting where the diffusion coefficient in the
convection-diffusion equation involved in the sys
tem is merely a bounded function with no additiona
l regularity. This necessitates the development of
a discrete counterpart of De Giorgi’s elliptic re
gularity theory\, which is then used\, in combinat
ion with various weak compactness techniques\, to
deduce the convergence of the sequence of numerica
l solutions to a weak solution of the system of pa
rtial differential equations. The theoretical resu
lt are illustrated by numerical experiments for a
model of the synovial fluid\, a non-Newtonian chem
ically-reacting incompressible fluid contained in
the cavities of human joints.
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Matthew Colbrook
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