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A Second Order Local Projection Lagrange-Galerkin Method for Navier-Stokes Equations at High Reynolds Numbers

  • Rodolfo Bermejo
  • Laura Saavedra
Chapter
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 8)

Abstract

We present a stabilized Backward Difference Formula of order 2- Lagrange Galerkin method for the incompressible Navier-Stokes equations at high Reynolds numbers. The stabilization of the conventional Lagrange-Galerkin method is done via a local projection technique for inf-sup stable finite elements. We have proven that for the Taylor-Hood finite element the a priori error estimate for velocity in the \(l^{\infty }(L^{2}(\varOmega )))\)-norm is O(h2 +Δ t2) whereas the error for the pressure in the l2(L2(Ω)))-norm is O(h2 +Δ t2), with error constants that are independent of the inverse of the Reynolds number. Numerical examples at high Reynolds numbers show the robustness of our method.

Keywords

High Reynolds Number Quadrature Rule Local Projection Material Derivative Finite Element Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada, E.T.S.I. IndustrialesUniversidad Politécnica de MadridMadridSpain
  2. 2.Departamento de Matemática Aplicada a la Ingeniería Aeroespacial, E.T.S.I. Aeronáutica y del EspacioUniversidad Poliécnica de MadridMadridSpain

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