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Séminaire d’Analyse Numérique et Calcul Scientifique

par alozinski - publié le , mis à jour le

Le séminaire a lieu le jeudi, à 11h, en salle 316 du bâtiment de
Métrologie (plan d’accès).

Vous trouverez ci-dessous le planning du séminaire
d’Analyse Numérique et Calcul Scientifique pour l’année universitaire en cours.

Pour contacter le responsable (Alexei Lozinski) :
alexei.lozinski@univ-fcomte.fr.

Exposés à venir :

  • Jeudi 19 octobre 2016, à 11h : Samuel Dubuis (EPFL)
    Annulé
    An adaptive algorithm for the time dependent transport equation with anisotropic finite elements and the Crank-Nicolson scheme

    The time dependent transport equation is solved with stabilized continuous, piecewise linear finite elements and the Crank-Nicolson scheme [1]. Finite elements with large aspect ratio are advocated in order to account for boundary layers. The error due to space discretization has already been studied in [2]. Here, the error due to the use of the Crank-Nicolson scheme is taken into account. Anisotropic a priori and a posteriori error estimates are proved. The a posteriori upper bound is obtained using a quadratic reconstruction in time as in [3].
    The quality of the error estimator is first validated on non adapted meshes and constant time steps. An adaptive algorithm in space and time is then proposed, with goal to build a sequence of anisotropic meshes and time steps, so that the final error is close to a preset tolerance. Numerical results on adapted, anisotropic meshes and
    time steps show the efficiency of the method.

    [1] E. Burman, Consistent SUPG-method for transient transport problems : Stability
    and convergences, Comput. Methods Appl. Mech. Engrg., 199 (2010).
    [2] Y. Bourgault and M. Picasso, Anisotropic error estimates and space adaptivity for a semidiscrete finite element approximation of the transient transport equation SIAM J. Sci. Comput., 35 (2013).
    [3] A. Lozinski, M.Picasso and V. Prachittham, An anisotropic error estimator for the Crank-Nicolson method : application to a parabolic problem, SIAM J. Sci. Comput., 31 (2009).

Exposés passés :

Agenda

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