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Static Two-Grid Mixed Finite-Element Approximations to the Navier-Stokes Equations

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Abstract

A two-grid scheme based on mixed finite-element approximations to the incompressible Navier-Stokes equations is introduced and analyzed. In the first level the standard mixed finite-element approximation over a coarse mesh is computed. In the second level the approximation is post processed by solving a discrete Oseen-type problem on a finer mesh. The two-level method is optimal in the sense that, when a suitable value of the coarse mesh diameter is chosen, it has the rate of convergence of the standard mixed finite-element method over the fine mesh. Alternatively, it can be seen as a post processed method in which the rate of convergence is increased by one unit with respect to the coarse mesh. The analysis takes into account the loss of regularity at initial time of the solution of the Navier-Stokes equations in absence of nonlocal compatibility conditions. Some numerical experiments are shown.

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Authors and Affiliations

  1. IMUVA, Instituto de Matemáticas, Universidad de Valladolid, Valladolid, Spain

    Javier de Frutos

  2. Departamento de Matemática Aplicada II, Universidad de Sevilla, Sevilla, Spain

    Bosco García-Archilla

  3. Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain

    Julia Novo

Authors
  1. Javier de Frutos
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  2. Bosco García-Archilla
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  3. Julia Novo
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Corresponding author

Correspondence to Julia Novo.

Additional information

Research of J. de Frutos was supported by Spanish MEC under grant MTM2010-14919 and by JCyL under grant VA001A10-1.

Research of B. García-Archilla was supported by Spanish MEC under grant MTM2009-07849.

Research of J. Novo was supported by Spanish MEC under grant MTM2010-14919.

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de Frutos, J., García-Archilla, B. & Novo, J. Static Two-Grid Mixed Finite-Element Approximations to the Navier-Stokes Equations. J Sci Comput 52, 619–637 (2012). https://doi.org/10.1007/s10915-011-9562-7

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  • DOI: https://doi.org/10.1007/s10915-011-9562-7

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