Numerical approximation of stiff transmission problems by mixed finite element methods
Capatina-Papaghiuc, Daniela ; Raynaud, Nicolas
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 32 (1998), p. 611-629 / Harvested from Numdam
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@article{M2AN_1998__32_5_611_0,
     author = {Capatina-Papaghiuc, Daniela and Raynaud, Nicolas},
     title = {Numerical approximation of stiff transmission problems by mixed finite element methods},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {32},
     year = {1998},
     pages = {611-629},
     mrnumber = {1643477},
     zbl = {0907.73054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1998__32_5_611_0}
}

Capatina-Papaghiuc, Daniela; Raynaud, Nicolas. Numerical approximation of stiff transmission problems by mixed finite element methods. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 32 (1998) pp. 611-629. http://gdmltest.u-ga.fr/item/M2AN_1998__32_5_611_0/

[1] V. Andreev, S. Samarsky (1978) : Méthodes aux différences pour les équations elliptiques, Editions de Moscou. | MR 502018 | Zbl 0377.35004

[2] D. N. Arnold (1981): Discretization by finite elements of a model parameter dependent problem, Numer. Math., 37, 405-421. | MR 627113 | Zbl 0446.73066

[3] D. N. Arnold, F. Brezzi (1985): Mixed and nonconforming finite element methods: implementation, post-processing and error estimates, Mathematical Modelling and Numerical Analysis, 19, 7-32. | Numdam | MR 813687 | Zbl 0567.65078

[4] I. Babuška, M. Suri (1992): On locking and robustness in the finite element method, SIAM J. Numer. Anal., 29, 1261-1293. | MR 1182731 | Zbl 0763.65085

[5] A. Bayliss, E. Turkel (1980): Radiation boundary condition for wave-like equations, Comm. on Pure and Appl. Math., 13, 707-726. | MR 596431 | Zbl 0438.35043

[6] A. Bendali, K. Lemrabet (1997): The effect of a thin coating of a time-harmonic wave for the Helmholtz equation, SIAM J. of Applied Math. (to appear). | MR 1417476 | Zbl 0869.35068

[7] A. Bendali, N. Raynaud, J.-M. Thomas (1966): New decomposition of shape function spaces of mixed finite element methods, Applied Mathematics Letters, 9, 33-38. | MR 1389594 | Zbl 0854.65097

[8] F. Brezzi, M. Fortin (1991): Mixed and Hybrid Finite Element Methods, Springer Verlag, New York. | MR 1115205 | Zbl 0788.73002

[9] D. Caillerie (1980): The effect of a thin inclusion of high rigidity in an elastic body, Math. Meth. in the Appl. Sci., 2, 251-270. | MR 581205 | Zbl 0446.73014

[10] D. Capatina-Papaghiuc (1997): Contribution à la prévention du phénomène de verrouillage numérique, Thesis, Université de Pau, France.

[11] D. Chenais, J.-C. Paumier (1994): On the locking phenomenon for a class of elliptic problem, Numer. Math., 67, 427-440. | MR 1274440 | Zbl 0798.73054

[12] P. G. Ciarlet (1978): The Finite Element Method for Elliptic Problems, Studies in Mathematics and its Applications 4, North Holland, Amsterdam. | MR 520174 | Zbl 0383.65058

[13] P. Destuynder (1986): Une théorie asymptotique des plaques minces en élasticité linéaire, Collection RMA, Masson, Paris. | MR 830660 | Zbl 0627.73064

[14] B. Engquist, A. Majda (1977): Absorbing boundary conditions for the numerical simulation of waves, Math. Comp., 31, 629-651. | MR 436612 | Zbl 0367.65051

[15] B. Engquist, J.-C. Nedelec (1993): Effective boundary conditions for accoustic and electromagnetic scattering in thin layers, Rapport Intern 278, École Polytechnique, Palaiseau.

[16] V. Girault, P. A. Raviart (1986) : Finite Element Methods for Navier-Stokes Equations, Springer Verlag, Berlin. | MR 851383 | Zbl 0585.65077

[17] M. D. Gunzburger (1989): Finite element methods for viscous incompressible flows, A guide to theory, practice and algorithms, Computer Science and Scientific Computing, Academic Press, San Diego. | MR 1017032 | Zbl 0697.76031

[18] H. Le Dret (1991): Problèmes variationnels dans les multi-domaines ; modélisation et applications, Collections RMA, Masson, Paris. | MR 1130395 | Zbl 0744.73027

[19] K. Lemrabet (1987): Étude de divers problèmes aux limites de Ventcel d'origine physique ou mécanique dans des domaines non réguliers, Thesis, USTHB, Alger.

[20] K. Lemrabet (1977): Régularité de la solution d'un problème de transmission, J. Maths Pures et Appl., 56, 1-38. | MR 509312 | Zbl 0366.35036

[21] N. Raynaud (1994): Approximation par éléments finis de problèmes de transmission raide, Thesis, Université de Pau, France.

[22] J. E. Roberts, J. M. Thomas (1991): Mixed and Hybrid Methods, in Handbook of Numerical Analysis, vol. II: Finite Element Methods, P. G. Ciarlet & J. L. Lions editors, North Holland, Amsterdam, 523-639. | MR 1115239 | Zbl 0875.65090