Error estimates of a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations

Hirofumi Notsu, Masahisa Tabata

    Research output: Contribution to journalArticle

    12 Citations (Scopus)

    Abstract

    Error estimates with optimal convergence orders are proved for a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations. The scheme is a combination of Lagrange-Galerkin method and Brezzi-Pitkaranta'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 theoretical convergence orders are recognized numerically by two- and three-dimensional computations.

    Original languageEnglish
    Pages (from-to)361-380
    Number of pages20
    JournalMathematical Modelling and Numerical Analysis
    Volume50
    Issue number2
    DOIs
    Publication statusPublished - 2016 Mar 1

    Fingerprint

    Degrees of freedom (mechanics)
    Galerkin methods
    Linear equations
    Lagrange
    Galerkin
    Navier Stokes equations
    Error Estimates
    Navier-Stokes Equations
    Convergence Order
    Stabilization
    Lagrange Method
    Three-dimensional
    System of Linear Equations
    Galerkin Method
    Convection
    Degree of freedom
    Finite Element

    Keywords

    • Error estimates
    • Pressure-stabilization
    • The finite element method
    • The Lagrange-Galerkin method
    • The Navier-Stokes equations

    ASJC Scopus subject areas

    • Analysis
    • Numerical Analysis
    • Modelling and Simulation
    • Applied Mathematics

    Cite this

    Error estimates of a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations. / Notsu, Hirofumi; Tabata, Masahisa.

    In: Mathematical Modelling and Numerical Analysis, Vol. 50, No. 2, 01.03.2016, p. 361-380.

    Research output: Contribution to journalArticle

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