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H 1 Virtual element approximation of magnetostatic

Auteurs : Marini, Donatella (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We present a lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general decompositions of the computational domain (as is natural for Virtual Element Methods) and uses as unknowns the (constant) tangential component of the magnetic eld H on each edge, and the vertex values of the Lagrange multiplier p (used to enforce the solenoidality of the magnetic induction B = µH). In this respect the method can be seen as the natural generalization of the lowest order Edge Finite Element Method (the so-called ”first kind N´ed´elec” elements) to polyhedra of almost arbitrary shape, and as we show on some numerical examples it exhibits very good accuracy (for being a lowest order element) and excellent robustness with respect to distortions. Hints on a whole family of elements will also be given.

    Codes MSC :
    65N12 - Stability and convergence of numerical methods (BVP of PDE)
    65N30 - Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 28/05/2019
      Date de captation : 29/04/2019
      Collection : Research talks ; Numerical Analysis and Scientific Computing ; Partial Differential Equations
      Format : MP4
      Durée : 00:40:14
      Domaine : PDE ; Numerical Analysis & Scientific Computing
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-04-29_Marini.mp4

    Informations sur la rencontre

    Nom de la rencontre : POEMs - POlytopal Element Methods in Mathematics and Engineering
    Organisateurs de la rencontre : Antonietti, Paola ; Beirão da Veiga, Lourenço ; Di Pietro, Daniele ; Droniou, Jérôme ; Krell, Stella
    Dates : 29/04/2019 - 03/05/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/1954.html

    Citation Data

    DOI : 10.24350/CIRM.V.19528503
    Cite this video as: Marini, Donatella (2019). Virtual element approximation of magnetostatic. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19528503
    URI : http://dx.doi.org/10.24350/CIRM.V.19528503


    Voir aussi

    Bibliographie

    1. DA VEIGA, L. Beirao, BREZZI, F., DASSI, F., et al. Virtual element approximation of 2d magnetostatic problems. Computer Methods in Applied Mechanics and Engineering, 2017, vol. 327, p. 173-195. - https://doi.org/10.1016/j.cma.2017.08.013

    2. KIKUCHI, Fumio. Mixed formulations for finite element analysis of magnetostatic and electrostatic problems. Japan Journal of Applied Mathematics, 1989, vol. 6, no 2, p. 209. - DOI https://doi.org/10.1007/BF03167879ISTEX

    3. BEIRÃO DA VEIGA, L., BREZZI, F., DASSI, F., et al. A family of three-dimensional virtual elements with applications to magnetostatic. arXiv preprint arXiv:1804.10497, 2018. - https://arxiv.org/abs/1804.10497

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