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UID:8331@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140624T110000
DTEND;TZID=Europe/Paris:20140624T120000
DTSTAMP:20241120T210339Z
URL:https://www.i2m.univ-amu.fr/evenements/a-second-order-maximum-principl
 e-preserving-continuous-finite-element-technique-for-nonlinear-scalar-cons
 ervation-equations/
SUMMARY: (...): A second-order maximum principle preserving continuous fini
 te  element technique for nonlinear scalar conservation equations
DESCRIPTION:: In the first part of the talk I will introduces a first-order
  viscosity method for the explicit approximation of scalar conservation eq
 uations with Lipschitz fluxes using continuous finite elements on arbitrar
 y grids in any space dimension. Provided the lumped mass matrix is positiv
 e definite\, the method is shown to satisfy the local maximum principle un
 der a usual CFL condition. The method is independent of the cell type\; fo
 r instance\, the mesh can be a combination of tetrahedra\, hexahedra\, and
  prisms in three space dimensions. An a priori convergence estimate is giv
 en provided the initial data is BV.\nIn the second part of the talk I will
  extend the accuracy of the method to second-order (at least). The techniq
 ue is based on mass-lumping correction\, a high-order entropy viscosity me
 thod\, and the Boris-Book-Zalesak flux correction technique. The algorithm
  works for arbitrary meshes in any space dimension and for all Lipschitz f
 luxes.\nThe formal second-order accuracy of the method and its convergence
  properties are tested on a series of linear and nonlinear benchmark probl
 ems.\n\nhttp://www.math.tamu.edu/~guermond/\n\nJean-Luc Guermond\, Texas A
 &amp\;M University\n\n
CATEGORIES:Séminaire,Analyse Appliquée
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