Abstract
This paper is devoted to the steady-state, incompressible Navier-Stokes equations with non standard boundary conditions of the form: \(u \times n = 0 , p + (1/2)u \cdot u = 0 ,\), or \(u \cdot n = 0 , curl u \cdot n = 0 , curl curl u \cdot n = 0 ,\), or \(u \cdot n = 0 , curl u \times n = 0 .\).
The problem is formulated in the primitive variables : velocity and pressure, and the divergence-free condition is imposed weakly by the equation \(\left( {\bar Vq,v} \right) = 0.\).
Thus, while more regularity is required for the pressure, owing to the boundary conditions, the velocity needs only have a smooth curl. Hence, the velocity is approximated with curl conforming finite elements and the pressure with standard continuous finite elements. The error analysis gives optimal results.
This paper is in final form and no similar paper has been or is being submitted elsewhere.
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Girault, V. (1990). Curl-conforming finite element methods for Navier-Stokes equations with non-standard boundary conditions in ℜ3 . In: Heywood, J.G., Masuda, K., Rautmann, R., Solonnikov, V.A. (eds) The Navier-Stokes Equations Theory and Numerical Methods. Lecture Notes in Mathematics, vol 1431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086071
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DOI: https://doi.org/10.1007/BFb0086071
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