A Stabilized Finite Element Method for the Oseen Equation with Dominating Reaction

Gabriel Raúl Barrenechea Miguel Angel Fernández 1 Carolina Ivon Vidal
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : A new stabilized finite element method is introduced for the linearized version of the Navier-Stokes equation (or Oseen equation), containing a dominating zeroth order term. The method consists in subtracting a mesh dependent term from the formulation without compromising consistency. The design of this mesh dependent term, as well as the stabilization parameter involved, are suggested by bubble condensation. Stability is proved for any combination of velocity and pressure spaces, under the hypotheses of continuity for the pressure space. Optimal order error estimates are derived for the velocity and the pressure, using the standard norms for these unknowns. Numerical experiments confirming these theoretical results are presented.
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https://hal.inria.fr/inria-00070780
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Submitted on : Friday, May 19, 2006 - 9:36:40 PM
Last modification on : Tuesday, May 14, 2019 - 10:17:12 AM
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  • HAL Id : inria-00070780, version 1

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Gabriel Raúl Barrenechea, Miguel Angel Fernández, Carolina Ivon Vidal. A Stabilized Finite Element Method for the Oseen Equation with Dominating Reaction. [Research Report] RR-5213, INRIA. 2004, pp.21. ⟨inria-00070780⟩

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