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CATEGORIES:Applied Mathematics Seminar Series
SUMMARY:Optimal discretisation in Banach spaces - Dr Kris
van der Zee\, University of Nottingham
DTSTART:20161128T150000Z
DTEND:20161128T160000Z
UID:TALK2252AT
URL:/talk/index/2252
DESCRIPTION:Is it possible to obtain near-best approximations
to solutions of linear operator equations in a gen
eral Banach space setting? Can this be done with g
uaranteed stability?\n\nIn this seminar\, I addres
s these questions by considering nonstandard\, non
linear\, Petrov-Galerkin discretizations. These me
thods are particularly useful for PDEs with rough
data or nonsmooth solutions having discontinuities
.\n\nI build on ideas of residual minimization and
the recent theory of optimal Petrov-Galerkin meth
ods in Hilbert-space settings. I will demonstrate
that the implementable version of the Petrov-Galer
kin formulation is naturally related to a mixed me
thod with a monotone nonlinearity. In the setting
of certain special Banach spaces\, I will prove op
timal a priori error estimates (a la Cea / Babuska
)\, with constants depending on the geometry of th
e involved Banach spaces.\n\nThis is joint work wi
th Ignacio Muga of Pontificia Universidad Catolica
de Valparaiso.\n
LOCATION:Arts Lecture Room 1
CONTACT:David Smith
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