Abstract
We present an abstract stabilization method which covers previous concrete applications to advection-diffusion equations and to the Stokes equations for incompressible fluids. We then apply the method to stabilize domain decomposition formulations for elliptic problems. We obtain a method that allows the treatment of internal variables, interface variables and Lagrange multipliers (normal derivatives) by piecewise polynomials of arbitrary order.
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References
I. Babuška: The finite element method with lagrangian multipliers, Numer. Math., 20, 179–192, 1973.
C. Baiocchi and F. Brezzi: in preparation.
H.J.C. Barbosa, T.J.R. Hughes: Boundary Lagrange multipliers in finite element methods: error analysis in natural norms, Numer. Math., 62, 1–16, 1992.
C. Bernardi, Y. Maday and A.T. Patera: A new nonconforming approach to domain decompositions: The mortar element method. In Nonlinear Partial Differential Equations and their Applications (H.Brezis-J.L.Lions eds.), Pitman and Wiley, 1989.
F. Brezzi and M. Fortin: Mixed and hybrid finite element methods, Springer Verlag, New York 1991.
F. Brezzi and L.D. Marini: Macro hybrid elements and domain decomposition methods. (To appear in Proc. Colloque en l'honneur du 60ème anniversaire de Jean Cea, Sophia-Antipolis, April 1992).
F. Brezzi and L.D. Marini: A three-field domain decomposition method. (To appear in Proc. 6th International Conference on Domain Decomposition Methods in Science and Engineering, Como, June 1992).
F. Brezzi and L.D. Marini: in preparation.
J. Douglas, jr. and J. Wang: An absolutely stabilized finite element method for the Stokes problem, Math. Comp., 52, 495–508, 1989.
L.P. Franca and S.L. Frey: Stabilized finite element methods: II. The incompressible Navier-Stokes equations, (to appear in Comput. Meths. Appl. Mech. Engrg.).
L.P. Franca, S.L. Frey and T.J.R. Hughes: Stabilized finite element methods: I. Application to the advective-diffusive model, Comput. Meths. Appl. Mech. Engrg., 95, 253–276, 1992.
L.P. Franca and T.J.R. Hughes: Two classes of mixed finite element methods, Comput. Meths. Appl. Mech. Engrg., 69, 89–129, 1988.
L.P. Franca and R. Stenberg: Error analysis of some Galerkin least square methods for the elasticity equations, SIAM J. Numer. Anal., 28, 1680–1697, 1991.
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© 1992 Springer-Verlag Berlin Heidelberg
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Baiocchi, C., Brezzi, F., Marini, L.D. (1992). Stabilization of Galerkin methods and applications to domain decomposition. In: Bensoussan, A., Verjus, J.P. (eds) Future Tendencies in Computer Science, Control and Applied Mathematics. INRIA 1992. Lecture Notes in Computer Science, vol 653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56320-2_71
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DOI: https://doi.org/10.1007/3-540-56320-2_71
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