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Stabilization of a non standard FETI-DP mortar methodfor the Stokes problem

Published online by Cambridge University Press:  10 January 2014

E. Chacón Vera  and
T. Chacón Rebollo
E. Chacón Vera
Affiliation:
Dpto. Matemáticas, Facultad de Matemáticas, Universidad de Murcia, Campus Espinardo, 30100 Murcia, Spain. [email protected]
T. Chacón Rebollo
Affiliation:
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Tarfia sn., 41012 Sevilla, Spain; [email protected]
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Abstract

In a recent paper [E. Chacón Vera and D. Franco Coronil, J. Numer. Math. 20 (2012) 161–182.] a non standard mortar method for incompressible Stokes problem was introduced where the use of the trace spaces H1 / 2and H1/200and a direct computation of the pairing of the trace spaces with their duals are the main ingredients. The importance of the reduction of the number of degrees of freedom leads naturally to consider the stabilized version and this is the results we present in this work. We prove that the standard Brezzi–Pitkaranta stabilization technique is available and that it works well with this mortar method. Finally, we present some numerical tests to illustrate this behaviour.

Keywords

Incompressible Stokes problemnon-standard FETI-DP mortar method
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 1 , January 2014 , pp. 285 - 304
Copyright
© EDP Sciences, SMAI, 2014

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References

R.A. Adams, Sobolev Spaces. In vol. 65 of Pure and Applied Mathematics. Academic Press, New York, London (1975).
Braess, D., Dahmen, W. and Wieners, C., A multigrid algorithm for the mortar finite element method. SIAM J. Numer. Anal. 37 (1999) 48–69. Google Scholar
Ben Belgacem, F., The Mortar finite element method with Lagrange multipliers. Numerische Mathematik 84 (1999) 173–197. Google Scholar
Bernardi, C., Chacón Rebollo, T. and Chacón Vera, E., A FETI method with a mesh independent condition number for the iteration matrix. Comput. Methods Appl. Mech. Engrg. 197 (2008) 1410–1429. Google Scholar
C. Bernardi, Y. Maday and A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, edited by H. Brezis and J.-L. Lions. Collège de France Seminar XI, Pitman (1994) 13–51.
Chacón Vera, E., A continuous framework for FETI-DP with a mesh independent condition number for the dual problem. Comput. Methods Appl. Mech. Engrg. 198 (2009) 2470–2483. Google Scholar
Chacón Vera, E., and Franco Coronil, D., A non standard FETI-DP mortar method for Stokes Problem. Proceedings of the 3rd FreeFem++ days, Paris, 2011. J. Numer. Math. 20 (2012) 161–182. Google Scholar
http://www.freefem.org/ff++
L.P. Franca, T.J.R. Hughes and R. Stenberg, Stabilized Finite Element Methods, in Incompressible Computational Fluid Dynamics, chap. 4, edited by M. Gunzburger and R.A. Nicolaides. Cambridge Univ. Press, Cambridge (1993) 87–107.
V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms, vol. 5 of Springer Series in Comput. Math. Springer-Verlag, Berlin (1986).
P. Grisvard, Singularities in Boundary value problems, vol. 22 of Recherches en Mathématiques Appliquées, Masson (1992).
Lee, C.O. and Park, E.H., A dual iterative substructuring method with a penalty term, Numerische Mathematik V. 112 (2009) 89–113. Google Scholar
Raviart, P.A. and Thomas, J.-M., Primal Hybrid Finite Element Methods for second order elliptic equations. Math. Comput. 31 (1977) 391–413. Google Scholar