On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions

 Access to full text

 Full (PDF)

1. [1] Y. Achdou, R. Glowinski and O. Pironneau, Tuning the mesh of a mixed method for the stream function-vorticity formulation of the Navier-Stokes equations, Numer. Math. 63 (1992) 145-163. Zbl0760.76041MR1182970
2. [2] I. Babuška, The finite element method with Lagrange multipliers. Numer. Math. 20 (1973) 179-192. Zbl0258.65108MR359352
3. [3] C. Bernardi, Méthodes d'éléments finis mixtes pour les équations de Navier-Stokes. Thèse de 3e Cycle, Université de Paris VI, France (1979). 
4. [4] P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). Zbl0383.65058MR520174
5. [5] F. El Dabaghi and O. Pironneau, Stream vectors in three dimensional aerodynamics. Numer. Math. 48 (1986) 561-589. Zbl0625.76009MR839617
6. [6] V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer Verlag, Berlin (1986). Zbl0585.65077MR851383
7. [7] R. Glowinski and O. Pironneau, Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem. SIAM Rev. 21 (1979) 167-212. Zbl0427.65073MR524511
8. [8] P. Neittaanmaki and M. Krizek, in Efficient Solution of Elliptic Systems, Finite element approximation for a div-rot System with mixed boundary conditions in non-smooth plane domain. Notes in Numerical Fluid Mechanics, Vol. 10, W. Hachbush Ed., Vieweg Publishing, Wiesbaden, Germany (1984); see also Appl. Math. 29 (1984) 272-285. Zbl0575.65125MR754079
9. [9] L. Quartapelle, Numerical Solution of the Incompressible Navier-Stokes Equations. Birkhäuser, Basel (1993). Zbl0784.76020MR1266843
10. [10] L. Quartapelle and A. Muzzio, Decoupled solution of vector Poisson equations with boundary condition coupling, in Computional Fluid Dynamics, G. de Vahl Davis and C. Fletcher Eds., Elsevier Science Publishers B.V., North-Holland (1988) 609-619. 
11. [11] L. Quartapelle, V. Ruas and J. Zhu, Uncoupled solution of the three-dimensional vorticity-velocity equations. ZAMP 49 (1998) 384-400. Zbl0912.35124MR1629537
12. [12] V. Ruas, L. Quartapelle and J. Zhu, A symmetrized velocity-vorticity formulation of the three-dimensional Stokes system. C.R. Acad. Sci. Paris Sér. IIb 323 (1996) 819-824. Zbl0923.76033
13. [13] G. Strang and G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, New York (1973). Zbl0356.65096MR443377
14. [14] J. Zhu, A.F.D. Loula and L. Quartapelle, A vector Poisson problem with coupling boundary conditions in a Lipschitz 2D domain, Research Report, Laboratório Nacional de Computação Cientifica, CNPq, N° 30 (1997). 
15. [15] J. Zhu, A.F.D. Loula and L. Quartapelle, Finite element solution of vector Poisson equation with a coupling boundary condition. Numer. Methods Partial Differential Eq. 16 (2000). Zbl0956.65103MR1727582
16. [16] J. Zhu, L. Quartapelle and A.F.D. Loula, Uncoupled variational formulation of a vector Poisson problem. C.R. Acad. Sci.Paris Sér. I 323 (1996) 971-976. Zbl0869.76069MR1414568