Stabilization of a non standard FETI-DP mortar method for the Stokes problem
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 1, pp. 285-304.

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 H/ 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.

DOI : 10.1051/m2an/2013102
Classification : 65N30, 65N55
Mots-clés : incompressible Stokes problem, non-standard FETI-DP
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Chacón Vera, E.; Chacón Rebollo, T. Stabilization of a non standard FETI-DP mortar method for the Stokes problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 1, pp. 285-304. doi : 10.1051/m2an/2013102. http://archive.numdam.org/articles/10.1051/m2an/2013102/

[1] R.A. Adams, Sobolev Spaces. In vol. 65 of Pure and Applied Mathematics. Academic Press, New York, London (1975). | MR | Zbl

[2] D. Braess, W. Dahmen and C. Wieners, A multigrid algorithm for the mortar finite element method. SIAM J. Numer. Anal. 37 (1999) 48-69. | MR | Zbl

[3] F. Ben Belgacem, The Mortar finite element method with Lagrange multipliers. Numerische Mathematik 84 (1999) 173-197. | MR | Zbl

[4] C. Bernardi, T. Chacón Rebollo and E. Chacón Vera, A FETI method with a mesh independent condition number for the iteration matrix. Comput. Methods Appl. Mech. Engrg. 197 (2008) 1410-1429. | MR | Zbl

[5] 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. | MR | Zbl

[6] E. Chacón Vera, 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. | MR | Zbl

[7] E. Chacón Vera, and D. Franco Coronil, 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. | MR | Zbl

[8] http://www.freefem.org/ff++

[9] 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. | MR | Zbl

[10] 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). | MR | Zbl

[11] P. Grisvard, Singularities in Boundary value problems, vol. 22 of Recherches en Mathématiques Appliquées, Masson (1992). | MR | Zbl

[12] C.O. Lee and E.H. Park, A dual iterative substructuring method with a penalty term, Numerische Mathematik V. 112 (2009) 89-113. | MR | Zbl

[13] P.A. Raviart and J.-M. Thomas, Primal Hybrid Finite Element Methods for second order elliptic equations. Math. Comput. 31 (1977) 391-413. | MR | Zbl

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