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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Discontinuous Galerkin methods on arbitrarily shap
ed elements. - Emmanuil Georgoulis (University of
Leicester\; National Technical University of Athen
s)
DTSTART;TZID=Europe/London:20191022T111000
DTEND;TZID=Europe/London:20191022T115500
UID:TALK133096AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/133096
DESCRIPTION:We extend the applicability of the popular interio
r-penalty discontinuous Galerkin (dG) method discr
etizing advection-diffusion-reaction problems to m
eshes comprising extremely general\, essentially a
rbitrarily-shaped element shapes. In particular\,
our analysis allows for curved element shapes\, wi
thout the use of (iso-)parametric elemental maps.
The feasibility of the method relies on the defini
tion of a suitable choice of the discontinuity-pen
al-ization parameter\, which turns out to be essen
tially independent on the particular element shape
. A priori error bounds for the resulting method a
re given under very mild structural assumptions re
stricting the magnitude of the local curvature of
element boundaries. Numerical experiments are also
presented\, indicating the practicality of the pr
oposed approach. Moreover\, we shall discuss a num
ber of perspectives on the possible applications o
f the proposed framework in parabolic problems on
moving domains as well as on multiscale problems.
The above is an overview of results from joint wor
ks with A. Cangiani (Nottingham\, UK)\, Z. Dong (F
ORTH\, Greece / Cardiff UK) and T. Kappas (Leicest
er\, UK).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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