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SUMMARY:Discontinuous Galerkin methods on polygonal and polyhedral meshes
- Prof Emmanuil Georgoulis (University of Leicester & National Technical U
niversity of Athens)
DTSTART;VALUE=DATE-TIME:20180612T140000
DTEND;VALUE=DATE-TIME:20180612T150000
UID:https://talks.ox.ac.uk/talks/id/401f59f6-62aa-4afc-b8f6-dc7bc75e2d47/
DESCRIPTION:Numerical methods defined on computational meshes comprising o
f polygonal and/or polyhedral (henceforth collectively termed “polytopi
c") elements\, with\, potentially\, many faces\, have gained substantial t
raction recently for a number of important reasons. A key underlying issue
is the design of a suitable computational mesh upon which the underlying
PDE problem will be discretized. The task of generating the mesh must addr
ess two competing issues. The mesh should provide a good representation of
the given computational geometry with sufficient resolution for the accur
ate approximations. On the other hand\, the mesh should not be too fine\,
so that computational complexity becomes prohibitive due to the high numbe
r of numerical degrees of freedom. Standard mesh generators output grids c
onsisting of triangular/quadrilateral elements in 2D and tetrahedral/hexah
edral/prismatic/pyramidal elements in 3D. In the presence of essentially l
ower-dimensional solution features\, for example\, boundary/internal layer
s\, anisotropic meshing may be exploited. However\, in regions of high cur
vature\, the use of such highly-stretched elements may lead to element sel
f-intersection\, unless the curvature of the geometry is carefully ‘prop
agated’ into the interior of the mesh through the use of (computationall
y expensive) isoparametric element mappings. These issues are particularly
pertinent in the context of high-order methods\, since in this setting\,
accuracy is often achieved by exploiting coarse meshes in combination with
local high-order polynomial basis functions. I will argue that\, by drama
tically increasing the flexibility in terms of the set of admissible eleme
nt shapes present in the computational mesh\, the resulting discontinuous
Galerkin FEMs can potentially deliver dramatic savings in computational co
sts. Moreover\, if time permits\, I will present some recent theoretical d
evelopments in the error analysis of such methods. \n\nSpeakers:\nProf Em
manuil Georgoulis (University of Leicester & National Technical University
of Athens)
LOCATION:Information Engineering (LR7)\, Banbury Road OX1 3PH
URL:https://talks.ox.ac.uk/talks/id/401f59f6-62aa-4afc-b8f6-dc7bc75e2d47/
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DESCRIPTION:Talk:Discontinuous Galerkin methods on polygonal and polyhedra
l meshes - Prof Emmanuil Georgoulis (University of Leicester & National Te
chnical University of Athens)
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