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

Hirofumi Notsu, Masahisa Tabata

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    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.

    Original languageEnglish
    Title of host publicationMathematical Fluid Dynamics, Present and Future
    PublisherSpringer New York LLC
    Pages497-530
    Number of pages34
    Volume183
    ISBN (Print)9784431564553
    DOIs
    Publication statusPublished - 2016
    Event8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014 - Tokyo, Japan
    Duration: 2014 Nov 112014 Nov 14

    Other

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

    Fingerprint

    Error Estimates
    Navier-Stokes Equations
    Convergence Order
    Three-dimensional
    Second-order Accuracy
    Two-step Method
    System of Linear Equations
    Convection
    Stabilization
    Discretization
    Degree of freedom
    Trajectory
    Finite Element
    Fluid
    Derivative
    Numerical Results

    Keywords

    • Error estimates
    • Navier-Strokes equations
    • Second-order scheme
    • Stabilized Lagrange-Galerkin scheme

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Notsu, H., & Tabata, M. (2016). Error estimates of a stabilized lagrange–galerkin scheme of second-order in time for the navier–stokes equations. In Mathematical Fluid Dynamics, Present and Future (Vol. 183, pp. 497-530). Springer New York LLC. https://doi.org/10.1007/978-4-431-56457-7_18

    Error estimates of a stabilized lagrange–galerkin scheme of second-order in time for the navier–stokes equations. / Notsu, Hirofumi; Tabata, Masahisa.

    Mathematical Fluid Dynamics, Present and Future. Vol. 183 Springer New York LLC, 2016. p. 497-530.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Notsu, H & Tabata, M 2016, Error estimates of a stabilized lagrange–galerkin scheme of second-order in time for the navier–stokes equations. in Mathematical Fluid Dynamics, Present and Future. vol. 183, Springer New York LLC, pp. 497-530, 8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014, Tokyo, Japan, 14/11/11. https://doi.org/10.1007/978-4-431-56457-7_18
    Notsu H, Tabata M. Error estimates of a stabilized lagrange–galerkin scheme of second-order in time for the navier–stokes equations. In Mathematical Fluid Dynamics, Present and Future. Vol. 183. Springer New York LLC. 2016. p. 497-530 https://doi.org/10.1007/978-4-431-56457-7_18
    Notsu, Hirofumi ; Tabata, Masahisa. / Error estimates of a stabilized lagrange–galerkin scheme of second-order in time for the navier–stokes equations. Mathematical Fluid Dynamics, Present and Future. Vol. 183 Springer New York LLC, 2016. pp. 497-530
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