Numerical methods for a model for wave propagation in composite anisotropic media
Lovera, Oscar Mario ; Santos, Juan Enrique
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 22 (1988), p. 159-176 / Harvested from Numdam
Publié le : 1988-01-01
@article{M2AN_1988__22_1_159_0,
     author = {Lovera, Oscar Mario and Santos, Juan Enrique},
     title = {Numerical methods for a model for wave propagation in composite anisotropic media},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {22},
     year = {1988},
     pages = {159-176},
     mrnumber = {934705},
     zbl = {0663.76094},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1988__22_1_159_0}
}
Lovera, Oscar Mario; Santos, Juan Enrique. Numerical methods for a model for wave propagation in composite anisotropic media. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 22 (1988) pp. 159-176. http://gdmltest.u-ga.fr/item/M2AN_1988__22_1_159_0/

[1] F. Brezzi, J. Douglas Jr., and L.D. Marini, Two families of Mixed Finite Elements for Second Order Elliptic Problems, Numerische Mathematik, vol. 47 (1985), pp. 217.235. | MR 799685 | Zbl 0599.65072

[2] F. Brezzi, J. Douglas Jr., R. Durand and M. Fortin, Mixed Finite Elements for Second Order Elliptic Problems in Three Variables, Numerische Mathematik. 51 (1987), pp. 237-250. | MR 890035 | Zbl 0631.65107

[3] M.A. Biot, Theory of Propargation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range, Journal of the Acoustical Society of America, vol. 28, Number 2 (1956), pp. 168-179. | MR 134056

[4] M. A. Biot and D. G. Willis, The Elastic Coefficients of the Theory of Consolidation, Journal of Applied Mechanics, Vol. 24, Trans. Asme., vol. 79, (1957), pp. 594-601. | MR 92472

[5] M. A. Biot, Mechanics of Deformation and Acoustic Propagation in Porous Media, Journal of Applied Physics, vol. 33, Number 4 (1962), pp. 1482-1498. | MR 152238 | Zbl 0104.21401

[6] J. Douglas Jr., and J. E. Roberts, Global Estimates for Mixed Methods for Second Order Elliptic Equations, Mathematics of Computation, vol. 44 (1985), pp. 39-52. | MR 771029 | Zbl 0624.65109

[7] G. Duvaut and J. L. Lions, Inequalities in Mechanics and Physics, Springer-Verlag, Berlin, 1976. | MR 521262 | Zbl 0331.35002

[8] G. Fichera, Existence Theorems in Elasticity-Boundary Value Problems of Elasticity with Unilateral Constrains, Encyclopedia of Physics, S. Flüge, Ed., vol. 22, n° 1, 1988 vol.VIa/2: Mechanics of Solids II, C. Truesdell Ed., Springer-Verlag, Berlin, 1972, pp. 347-424.

[9] V. Girault and P. A. Raviart, Finite Element Approximation of the Navier- Stokes Equations, Springer-Verlag, Berlin, 1981. | MR 548867 | Zbl 0441.65081

[10]A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Dover, New York, Fourth Edition. | JFM 53.0752.01 | Zbl 0063.03651

[11] O. M. Lovera, Boundary Conditions for a Fluid-Saturated Porous Solid, Geophysics, 52 (1987), pp. 174-178.

[12] J. Lysmer and R. L. Kuhlemeyer, Finite Dynamic Model for Infinite Media, Journal Eng. Mech. Division, Proc. Amer. Soc. Civil Eng., 95 (1969), pp. 859-877.

[13] J. C. Nedelec, Mixed Finite Elements in R 3 , Numerische Mathematik, 35 (1980), pp. 325-341. | MR 592160 | Zbl 0419.65069

[14] J.A. Nitsche, On Korn's Second Inequality, R.A.I.R.O. Anal. Numer., 15 (1981), pp. 237-248. | Numdam | MR 631678 | Zbl 0467.35019

[15] P.A. Raviart and J. M. Thomas, A Mixed Finite Element Method for 2en Order Elliptic Problems, Mathematical Aspects of the Finite Element Method, Lecture Notes in Mathematics 606, Springer-Verlag, Berlin, 1977. | MR 483555 | Zbl 0362.65089

[16] J. E. Santos, Finite Element Methods for the Simulation of Ware Propagation in Two-dimensional Inhomogeneous Elastic Media, Calcolo, 22 (1985), pp. 249-317. | MR 859084 | Zbl 0592.73039

[17] J. E. Santos, Elastic Wave Propagatin in Fluid-Saturated Porous Media. Part I. The Existence and Uniqueness Theorems, Modélisation Mathématique et Analyse Numérique, vol. 20 (1986), pp. 113-128. | Numdam | MR 844519 | Zbl 0616.76104

[18] J. E. Santos and E. J. Orena, Elastic Wave Propagation in Fluid-Saturated Porous Media. Part II. The Galerkin Procedures, Modélisation Mathématique et Analyse Numérique, vol. 20 1986(), pp. 129-139. | Numdam | MR 844520 | Zbl 0616.76105

[19] J. E. Santos, J. Douglas Jr., and A. P. Calderon, Finite Element Methods for a Composite Model in Elastodynamics, to appear in SIAM J. Numer. Anal. | MR 942205 | Zbl 0684.73034

[20] J. M. Thomas, Sur l'Analyse Numérique des Méthodes d'Éléments Finis Hybrides et Mixtes, Thèse, Université P. et M. Curie, Paris, 1977.