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Project ID: ICA3-CT-2000-30007
Funded under: FP5-INCO 2
Country: France

A stabilized finite element method for quasi-stokes problems: Application to Navier-Stokes equations

We present a mixed finite element method to solve numerically the two dimensional Quasi­ Stokes equations. The aim is to use this method as a basic solver for the unsteady Navier­Stokes equations; to linearize these Navier­Stokes equations, the total derivative term of the velocity is treated with a first order characteristics method. The unknowns of the mixed Quasi­Stokes formulation are the vorticity and the stream function discretized by piecewise continuous functions. As well known a direct approach leading to the loss of one order in the error estimates, we use a regularization stabilization technique by adding a new discrete form in the formulation. This new formulation remains consistent and is inconditionaly convergent. Moreover, in case of sufficient regularity on the vorticity, we get an O(h) optimal error estimate. Numerical tests confirm the results announced in this theoretical part.

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Institut National de Recherche en Informatique et en Automatique - INRIA
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