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Two‐Level Brezzi‐Pitkäranta Discretization Method Based on Newton Iteration for Navier‐Stokes Equations with Friction Boundary Conditions

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  • Rong An
  • Xian Wang

Abstract

We present a new stabilized finite element method for Navier‐Stokes equations with friction slip boundary conditions based on Brezzi‐Pitkäranta stabilized method. The stability and error estimates of numerical solutions in some norms are derived for standard one‐level method. Combining the techniques of two‐level discretization method, we propose two‐level Newton iteration method and show the stability and error estimate. Finally, the numerical experiments are given to support the theoretical results and to check the efficiency of this two‐level iteration method.

Suggested Citation

  • Rong An & Xian Wang, 2014. "Two‐Level Brezzi‐Pitkäranta Discretization Method Based on Newton Iteration for Navier‐Stokes Equations with Friction Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:474160
    DOI: 10.1155/2014/474160
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    References listed on IDEAS

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    1. Yuan Li & Rong An, 2013. "Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-17, July.
    2. Yuan Li & Rong An, 2013. "Two‐Level Iteration Penalty Methods for the Navier‐Stokes Equations with Friction Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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