Error Estimates of a Pressure-Stabilized Characteristics Finite Element Scheme for the Oseen Equations

Hirofumi Notsu, Masahisa Tabata

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    15 Citations (Scopus)

    Abstract

    Error estimates with the optimal convergence order are proved for a pressure-stabilized characteristics finite element scheme for the Oseen equations. The scheme is a combination of Lagrange–Galerkin finite element method and Brezzi–Pitkäranta’s stabilization method. The scheme 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 order is recognized by two- and three-dimensional numerical results.

    Original languageEnglish
    Pages (from-to)940-955
    Number of pages16
    JournalJournal of Scientific Computing
    Volume65
    Issue number3
    DOIs
    Publication statusPublished - 2015 Feb 4

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    Keywords

    • Error estimates
    • Pressure-stabilization
    • The finite element method
    • The method of characteristics
    • The Oseen equations

    ASJC Scopus subject areas

    • Software
    • Computational Theory and Mathematics
    • Theoretical Computer Science
    • Engineering(all)

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