Analysis of a sequential regularization method for the unsteady Navier-Stokes equations

Xiliang Lu, Ping Lin, Jian-Guo Liu

    Research output: Contribution to journalArticle

    12 Citations (Scopus)

    Abstract

    The incompressibility constraint makes Navier-Stokes equationsdifficult. A reformulation to a better posed problem is needed before solving itnumerically. The sequential regularization method (SRM) is a reformulation which combines the penalty method with a stabilization method in the context of constrained dynamical systems and has the benefit of both methods. In the paper, we study the existence and uniqueness for the solution of the SRM and provide a simple proof of the convergence of the solution of the SRM to the solution of the Navier-Stokes equations. We also give error estimates for the time discretized SRM formulation.
    Original languageEnglish
    Pages (from-to)1476-1494
    Number of pages19
    JournalMathematics of Computation
    Volume77
    Issue number263
    DOIs
    Publication statusPublished - 2008

    Keywords

    • Navier-Stokes equations
    • Iterative penalty method
    • Implicit parabolic PDE
    • Error estimates
    • Constrained dynamical system
    • Stabilization method

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