Geodesic
The penalty method of grids matching in the mixed Herrmann--Miyoshi scheme
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 3, pp. 297-312.

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The penalty method for mixed finite element methods is formulated and studied. The Herrmann–Miyoshi scheme for the biharmonic equation is considered. The main idea is to construct a perturbation problem with two parameters that play the role of penalties. The perturbation problem is constructed by substitution of the main conditions in the mixed variational formulation on the interface by natural conditions that contain parameters. The discretization of the perturbation problem by the finite element method is done. Estimates of the norm of a difference between the solution of a discrete perturbation problem and that of a given problem are obtained. Recommendations for choosing penalties depending on a mesh size and penalties are given. 
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L. V. Maslovskaya; O. M. Maslovskaya. The penalty method of grids matching in the mixed Herrmann--Miyoshi scheme. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 3, pp. 297-312. http://geodesic.mathdoc.fr/item/SJVM_2009_12_3_a5/

[1] Babuska I., “Eroor-bounds for fnite element method”, Numer. Math., 16 (1971), 322–333 | DOI | MR | Zbl

[2] Nitsche J. A., “Convergence of nonconforming methods”, Math. Aspects of Finite Elements in Partial Differential Equations, Academic Press, New York, 1974, 15–53 | MR

[3] Becker R., Hansbo P., and Stenberg R., “A finite element method for domain decomposition with non-matching grids”, Math. Modelling and Numerical Analysis, 37:2 (2003), 209–225 | DOI | MR | Zbl

[4] Le Tallec P., Sassi T., “Domain decomposition with nonmatching grids: augmented Lagrangian approach”, Math. Comp., 64 (1995), 1367–1396 | DOI | MR | Zbl

[5] Babuska I., “The finite element method with penalty”, Math. Comp., 27 (1973), 221–228 | DOI | MR | Zbl

[6] Aubin J. P., “Approximation des problemes aux limites non homogenes et regularite de la convergence”, Calcolo, 6 (1969), 117–139 | DOI

[7] Maslovskaya L. V., Maslovskaya O.M., “Metod shtrafa dlya stykovki setok v metode konechnykh elementov”, Izvestiya vuzov. Matematika, 2006, no. 10, 33–43 | MR

[8] Maslovskaya L. V., Maslovskaya O. M., “Nekotorye metody stykovki setok v metode konechnykh elementov”, Materialy Sedmogo Vserossiiskogo seminara: Setochnye metody dlya kraevykh zadach i prilozheniya (Kazan, 21–24 sentyabrya 2007), 186–189

[9] Brezzi F., Raviart P. A., “Mixed finite element methods for 4th order elliptic equations”, Topics in Numerical Analysis III, Academic Press, New York, 1977, 33–56 | MR | Zbl

[10] Falk R. S., Osborn J. E., “Error estimates for mixed methods”, R.A.I.R.O. Analyse Numerique, 14:3 (1980), 249–277 | MR | Zbl

[11] Babuska I., Osborn J., and Pitkaranta J., “Analysis of mixed methods using mesh dependent norms”, Math. Comp., 35 (1980), 1039–1062 | DOI | MR | Zbl

[12] Maslovskaya L. V., “Povedenie resheniya bigarmonicheskogo uravneniya v oblastyakh s uglovymi tochkami”, Differentsialnye uravneniya, 19:12 (1983), 2172–2175 | MR | Zbl

[13] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, 1-e izd., Mir, M., 1980 | MR

[14] Brezzi F., “On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers”, R.A.I.R.O., R2, 8 (1974), 129–151 | MR | Zbl