Error estimates of a stabilized lagrange–galerkin scheme of second-order in time for the navier–stokes equations

Hirofumi Notsu, Masahisa Tabata

    研究成果: Conference contribution

    2 被引用数 (Scopus)

    抄録

    Error estimates with optimal convergence orders are proved for a stabilized Lagrange–Galerkin scheme of second-order in time for the Navier–Stokes equations. The scheme is a combination of Lagrange–Galerkin method and Brezzi– Pitkäranta's stabilization method. It maintains the advantages of both methods; (i) It is robust for convection-dominated problems and the system of linear equations to be solved is symmetric. (ii) Since the P1 finite element is employed for both velocity and pressure, the number of degrees of freedom is much smaller than that of other typical elements for the equations, e.g., P2/P1. Therefore, the scheme is efficient especially for three-dimensional problems. The second-order accuracy in time is realized by Adams-Bashforth's (two-step) method for the discretization of the material derivative along the trajectory of fluid particles. The theoretical convergence orders are recognized by two- and three-dimensional numerical results.

    本文言語English
    ホスト出版物のタイトルMathematical Fluid Dynamics, Present and Future
    出版社Springer New York LLC
    ページ497-530
    ページ数34
    183
    ISBN(印刷版)9784431564553
    DOI
    出版ステータスPublished - 2016
    イベント8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014 - Tokyo, Japan
    継続期間: 2014 11 112014 11 14

    Other

    Other8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014
    国/地域Japan
    CityTokyo
    Period14/11/1114/11/14

    ASJC Scopus subject areas

    • 数学 (全般)

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