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Finite element solution of vector Poisson equation with a coupling boundary condition. (English) Zbl 0956.65103
The authors study the boundary value problems for the vector Poisson equation with boundary conditions that include the divergence of the unknown vector function. Variational formulation and finite element approximation are presented. A convergence analysis of the numerical schemes is provided together with some numerical results.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
Full Text: DOI
[1] Zhu, C R Acad Sci Paris 323 pp 971– (1996)
[2] and A vector Poisson problem with coupling boundary conditions in a Lipschitz 2D domain, LNCC/CNPq Tech Rept 30, 1997.
[3] Méthodes d’éléments finis mixtes pour les equations de Navier-Stokes, Thèse de 3ème Cycle, Université de Paris VI, 1979.
[4] El Dabaghi, Numer Math 48 pp 561– (1986)
[5] Numerical solution of the incompressible Navier-Stokes equations, Birkhäuser, Basel, 1993. · doi:10.1007/978-3-0348-8579-9
[6] and ?Efficient solution of elliptic systems,? Notes in numerical fluid mechanics, Vol. 10, editor, Vieweg, Wiesbaden, 1984.
[7] and ?Decoupled solution of vector Poisson equations with boundary condition coupling,? Computional fluid dynamics, and editors, Elsevier North-Holland, Amsterdam, 1988, pp. 609-619.
[8] and Finite element analysis of the vector Poisson problem, Proc Joint Conf Italian Grp Comp Mech Ibero-Latin Am Assoc Comp Meth Eng, Univ Padova, 1996.
[9] Glowinski, SIAM Rev 21 pp 167– (1979)
[10] and Finite element methods for Navier-Stokes equations, Springer-Verlag, Berlin, 1986. · Zbl 0585.65077 · doi:10.1007/978-3-642-61623-5
[11] The finite element method for elliptic problems, North-Holland, Amsterdam, 1978.
[12] and An analysis of the finite element method, Prentice-Hall, Englewood Cliffs, NJ, 1973.
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