Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
Feistauer, Miloslav ; Sobotíková, Veronika
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 24 (1990), p. 457-500 / Harvested from Numdam
@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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {24},
     year = {1990},
     pages = {457-500},
     mrnumber = {1070966},
     zbl = {0712.65097},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1990__24_4_457_0}
}
Feistauer, Miloslav; Sobotíková, Veronika. Finite element approximation of nonlinear elliptic problems with discontinuous coefficients. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 24 (1990) pp. 457-500. http://gdmltest.u-ga.fr/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 999834 | Zbl 0679.35035

[2] P. G. Ciarlet, The Finite Element Method for Elliptic Problems. Amsterdam : North-Holland 1978. | MR 520174 | Zbl 0383.65058

[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 336957 | Zbl 0243.41004

[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 421108 | Zbl 0262.65070

[5] M. Feistauer, On irrotational flows through cascades of profiles in a layer of variable thickness. Apl. Mat. 29, 423-458 (1984). | MR 767495 | Zbl 0598.76061

[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 877102 | Zbl 0633.76025

[7] M. Feistauer, On the finite element approximation of a cascade flow problem. Numer. Mat.h 50, 655-684 (1987). | MR 884294 | Zbl 0646.76085

[8] M. Feistauer, A. Ženĺšek, Finite element solution of nonlinear elliptic problems. Numer. Math. 50, 451-475 (1987). | MR 875168 | Zbl 0637.65107

[9] M. Feistauer, A. Ženĺšek, Compactness method in the finite element theory of nonlinear elliptic problems. Numer. Math. 52, 147-163 (1988). | MR 923708 | Zbl 0642.65075

[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 413547 | Zbl 0288.65068

[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 0364.65104

[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 278544 | Zbl 0535.73084

[15] A. Kufner, O. John, S. Fucik, Function Spaces. Prague : Academia 1977. | MR 482102

[16] J. L. Lions, Quelques Methodes de Résolution des Problèmes aux Limites non Linéaires. Paris, Dunod 1969. | MR 259693 | Zbl 0189.40603

[17] A. Marrocco, Analyse numérique de problèmes d'éléctrotechnique. Ann. Sc.Math. Québec, vol. 1, 271-296 (1977). | MR 483548 | Zbl 0434.65093

[18] J. Nečas, Les Méthodes Directes en Théorie des Équations Elliptiques Prague, Academia 1967. | MR 227584

[19] J. Nečas, Introduction to the Theory of Nonlinear Elliptic Equations. Leipzig, Teubner Texte zur Mathematik, Band 52, 1983. | MR 731261 | Zbl 0526.35003

[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 388806 | Zbl 0306.35041

[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 221767 | Zbl 0199.50504

[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 251373 | Zbl 0151.15501

[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 413554 | Zbl 0264.65068

[25] A. Ženĺšek, Nonhomogeneous boundary conditions and curved triangular finite elements. Apl. Mat. 26, 121-141 (1981). | MR 612669 | Zbl 0475.65073

[26] A. Ženĺšek, Discrete forms of Friedrichs' inequalities in the finite element method. RAIRO Numer. Anal. 15, 265-286 (1981). | Numdam | MR 631681 | Zbl 0475.65072

[27] A. Ženĺšek, The finite element method for nonlinear elliptic equations with discontinuous coefficients. Preprint, Brno, 1988. | Zbl 0709.65081