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Convergence analysis of a residual local projection method for the Navier-Stokes equation

Araya, Rodolfa and Barrenechea, Gabriel and Poza, A. and Valentin, Frédéric (2012) Convergence analysis of a residual local projection method for the Navier-Stokes equation. SIAM Journal on Numerical Analysis, 50 (2). pp. 669-699. ISSN 0036-1429

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Abstract

This work presents and analyzes a new residual local projection stabilized finite element method (RELP) for the nonlinear incompressible Navier–Stokes equations. Stokes problems defined elementwise drive the construction of the residual-based terms which make the present method stable for the finite element pairs $\mathbb{P}_1/\mathbb{P}_l$, $l=0,1$. Numerical upwinding is incorporated through an extra control on the advective derivative and on the residual of the divergence equation. Well-posedness of the discrete problem as well as optimal error estimates in natural norms are proved under standard assumptions. Next, a divergence-free velocity field is provided by a simple postprocessing of the computed velocity and pressure using the lowest order Raviart–Thomas basis functions. This updated velocity is proved to converge optimally to the exact solution. Numerics assess the theoretical results and validate the RELP method.

Item type: Article
ID code: 39489
Keywords: Navier-Stokes equation, convergence analysis, residual local projection, Mathematics
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Pure Administrator
    Date Deposited: 03 May 2012 10:10
    Last modified: 03 May 2012 10:10
    URI: http://strathprints.strath.ac.uk/id/eprint/39489

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