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UID:3328@test.i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140624T110000
DTEND;TZID=Europe/Paris:20140624T120000
DTSTAMP:20200826T095911Z
URL:https://test.i2m.univ-amu.fr/events/a-second-order-maximum-principle-p
reserving-continuous-finite-element-technique-for-nonlinear-scalar-conserv
ation-equations/
SUMMARY:A second-order maximum principle preserving continuous finite elem
ent technique for nonlinear scalar conservation equations -
DESCRIPTION:In the first part of the talk I will introduces a first-order v
iscosity method for the explicit approximation of scalar conservation equa
tions with Lipschitz fluxes using continuous finite elements on arbitrary
grids in any space dimension. Provided the lumped mass matrix is positive
definite\, the method is shown to satisfy the local maximum principle unde
r a usual CFL condition. The method is independent of the cell type\; for
instance\, the mesh can be a combination of tetrahedra\, hexahedra\, and p
risms in three space dimensions. An a priori convergence estimate is given
provided the initial data is BV.\nIn the second part of the talk I will e
xtend the accuracy of the method to second-order (at least). The technique
is based on mass-lumping correction\, a high-order entropy viscosity meth
od\, and the Boris-Book-Zalesak flux correction technique. The algorithm w
orks for arbitrary meshes in any space dimension and for all Lipschitz flu
xes.\nThe formal second-order accuracy of the method and its convergence p
roperties are tested on a series of linear and nonlinear benchmark problem
s.\n\nhttp://www.math.tamu.edu/~guermond/\n\nJean-Luc Guermond\, Texas A&a
mp\;M University\n\n
CATEGORIES:Séminaire Analyse Appliquée (AA)
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DTSTART:20140330T030000
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