Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
ESAIM: Modélisation mathématique et analyse numérique, Tome 24 (1990) no. 4, pp. 457-500.
@article{M2AN_1990__24_4_457_0,
     author = {Feistauer, Miloslav and Sobot{\'\i}kov\'a, Veronika},
     title = {Finite element approximation of nonlinear elliptic problems with discontinuous coefficients},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {457--500},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {24},
     number = {4},
     year = {1990},
     mrnumber = {1070966},
     zbl = {0712.65097},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1990__24_4_457_0/}
}
TY  - JOUR
AU  - Feistauer, Miloslav
AU  - Sobotíková, Veronika
TI  - Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1990
SP  - 457
EP  - 500
VL  - 24
IS  - 4
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1990__24_4_457_0/
LA  - en
ID  - M2AN_1990__24_4_457_0
ER  - 
%0 Journal Article
%A Feistauer, Miloslav
%A Sobotíková, Veronika
%T Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1990
%P 457-500
%V 24
%N 4
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1990__24_4_457_0/
%G en
%F M2AN_1990__24_4_457_0
Feistauer, Miloslav; Sobotíková, Veronika. Finite element approximation of nonlinear elliptic problems with discontinuous coefficients. ESAIM: Modélisation mathématique et analyse numérique, Tome 24 (1990) no. 4, pp. 457-500. http://www.numdam.org/item/M2AN_1990__24_4_457_0/

[1] L. Boccardo,G. Buttazzo, Quasilinear elliptic equations with discontinuons coefficients. Universita Degli Studi Di Piza, Dipartimento Di Matematica, Luglio 1987, Numero 206. | MR | Zbl

[2] P. G. Ciarlet, The Finite Element Method for Elliptic Problems. Amsterdam : North-Holland 1978. | MR | Zbl

[3] P. G. Ciarlet, P. A. Raviart, General Lagrange and Hermite interpolation in Rn with applications to finite element methods. Arch. Rational Mech. Anal. 46, 177-199 (1972). | MR | Zbl

[4] P. G. Ciarlet,P. A. Raviart, The combined effect of curved boundaries and numerical integration in isoparametric finite element method. In :The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, ed. ), pp 409-474. New York : Academie Press 1972. | MR | Zbl

[5] M. Feistauer, On irrotational flows through cascades of profiles in a layer of variable thickness. Apl. Mat. 29, 423-458 (1984). | MR | Zbl

[6] M. Feistauer, Mathematical and numerical study of nonlinear problems in fluid mechanics. In : Proc. Conf. Equadiff 6, Brno 1985. (J. Vosmanský, M. Zlámal, eds. ), pp. 3-16, Berlin-Heidelberg : Springer 1986. | MR | Zbl

[7] M. Feistauer, On the finite element approximation of a cascade flow problem. Numer. Mat.h 50, 655-684 (1987). | MR | Zbl

[8] M. Feistauer, A. Ženĺšek, Finite element solution of nonlinear elliptic problems. Numer. Math. 50, 451-475 (1987). | MR | Zbl

[9] M. Feistauer, A. Ženĺšek, Compactness method in the finite element theory of nonlinear elliptic problems. Numer. Math. 52, 147-163 (1988). | MR | Zbl

[10] R. Glowinski, A. Marrocco, Analyse numérique du champ magnétique d'un alternateur par éléments finis et surrelaxation ponctuelle non lineaire. Comput. Methods Appl. Mech. Eng. 3, 55-85 (1974). | MR | Zbl

[11] R. Glowinski, A. Marrocco, Numerical solution of two-dimensional magnetostatic problems by augmented Lagrangian methods. Comput. Methods Appl. Mech. Eng. 12, 33-46 (1977). | Zbl

[12] V. Hruskova-Sobotikova, Numerical solution of nonlinear elliptic problems by the methods of the finite elements least squares and conjugate gradients. Thesis. Faculty of Mathematics and Physics, Charles University, Prague, 1987 (in Czech ).

[13] V. P. Il'In, Singularities of weak solutions to elliptic boundary values problems with discontinuous coefficients at higher derivatives. Zapiski Naucnych Seminarov LOMI AN SSSR, T. 38, Leningrad 1973 (in Russian).

[14] V. Kreisinger, J. Adam, Magnetic fields in nonlinear anisotropic ferromagnetics. Acta Technica CSAV, 209-241 (1984). | MR | Zbl

[15] A. Kufner, O. John, S. Fucik, Function Spaces. Prague : Academia 1977. | MR

[16] J. L. Lions, Quelques Methodes de Résolution des Problèmes aux Limites non Linéaires. Paris, Dunod 1969. | MR | Zbl

[17] A. Marrocco, Analyse numérique de problèmes d'éléctrotechnique. Ann. Sc.Math. Québec, vol. 1, 271-296 (1977). | MR | Zbl

[18] J. Nečas, Les Méthodes Directes en Théorie des Équations Elliptiques Prague, Academia 1967. | MR

[19] J. Nečas, Introduction to the Theory of Nonlinear Elliptic Equations. Leipzig, Teubner Texte zur Mathematik, Band 52, 1983. | MR | Zbl

[20] L. A. Oganesjan, L. A. Dmitrenko, Solution of elliptic equations with discontinuous coefficients on a regular mesh. ZVMMF, 14, No 4 (1974) (in Russian). | MR | Zbl

[21] V. J. Rivkind, On the convergence estimates of homogeneous difference schemes for elliptic and parabolic equations with discontinuous coefficients. In : Proc « Problems of Mathematical Analysis », I, Leningrad Published by Leningrad State University, 1966 (in Russian). | MR | Zbl

[22] M. P. Sapagovas, Finite-difference method for quasilinear elliptic equations with discontinuons coefficients. ZVMMF, 5, No 4 (1965) (in Russian).

[23] G. Stampacchia, Équations elliptiques du second ordre a coefficients discontinus. Séminaire de Mathématiques Supérieures n° 16, Montréal : Les Presses de l'Université de Montréal, 1966. | MR | Zbl

[24] G. Strang, Variational crimes in the fïnite element method. In : The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. (A. K. Aziz, ed. ), pp. 689-710. New York, Academic Press 1972. | MR | Zbl

[25] A. Ženĺšek, Nonhomogeneous boundary conditions and curved triangular finite elements. Apl. Mat. 26, 121-141 (1981). | MR | Zbl

[26] A. Ženĺšek, Discrete forms of Friedrichs' inequalities in the finite element method. RAIRO Numer. Anal. 15, 265-286 (1981). | Numdam | MR | Zbl

[27] A. Ženĺšek, The finite element method for nonlinear elliptic equations with discontinuous coefficients. Preprint, Brno, 1988. | Zbl