On Error Estimates for a Variant of the Mixed Finite Element Method
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 2, pp. 44-53 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The mixed finite element method for the second order quasilinear elliptic problems with a strongly monotone and locally Lipschitz continuous operator is investigated. The error estimates are obtained in the case when the gradient of the required solution is chosen as an auxiliary variable in the construction of the mixed finite element method.
Keywords: quasilinear elliptic equation, mixed finite element method, error estimates.
@article{UZKU_2013_155_2_a3,
     author = {A. P. Gogin and M. M. Karchevsky},
     title = {On {Error} {Estimates} for a {Variant} of the {Mixed} {Finite} {Element} {Method}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {44--53},
     year = {2013},
     volume = {155},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2013_155_2_a3/}
}
TY  - JOUR
AU  - A. P. Gogin
AU  - M. M. Karchevsky
TI  - On Error Estimates for a Variant of the Mixed Finite Element Method
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2013
SP  - 44
EP  - 53
VL  - 155
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UZKU_2013_155_2_a3/
LA  - ru
ID  - UZKU_2013_155_2_a3
ER  - 
%0 Journal Article
%A A. P. Gogin
%A M. M. Karchevsky
%T On Error Estimates for a Variant of the Mixed Finite Element Method
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2013
%P 44-53
%V 155
%N 2
%U http://geodesic.mathdoc.fr/item/UZKU_2013_155_2_a3/
%G ru
%F UZKU_2013_155_2_a3
A. P. Gogin; M. M. Karchevsky. On Error Estimates for a Variant of the Mixed Finite Element Method. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 2, pp. 44-53. http://geodesic.mathdoc.fr/item/UZKU_2013_155_2_a3/

[1] Karchevskii M. M., “Ob odnom podkhode k postroeniyu smeshannykh skhem MKE dlya kvazilineinykh ellipticheskikh uravnenii”, Setochnye metody dlya kraevykh zadach i ikh prilozheniya, Materialy Pyatogo Vseros. seminara, Izd-vo Kazan. un-ta, Kazan, 2004, 108–111

[2] Fedotov A. E., Smeshannyi metod konechnykh elementov dlya kvazilineinykh ellipticheskikh uravnenii, Dis. \ldots kand. fiz.-matem. nauk, Kazan, 2007, 112 pp.

[3] Karchevskii M. M., “Ob otsenke pogreshnosti odnogo varianta smeshannogo metoda konechnykh elementov dlya kvazilineinykh ellipticheskikh uravnenii”, Setochnye metody dlya kraevykh zadach i prilozheniya, Materialy Devyatoi Vseros. konf., Otechestvo, Kazan, 2012, 220–222

[4] Karchevskii M. M., “Ob iteratsionnykh metodakh chislennoi realizatsii smeshannykh skhem dlya kvazilineinykh ellipticheskikh uravnenii vtorogo poryadka”, Issled. po prikl. matem. i informatike, 25, Izd-vo Kazan. un-ta, Kazan, 2004, 59–69

[5] Gogin A. P., Karchevskii M. M., “Ob iteratsionnykh metodakh dlya nekotorykh klassov smeshannykh skhem dlya kvazilineinykh ellipticheskikh uravnenii”, Setochnye metody dlya kraevykh zadach i prilozheniya, Materialy Devyatoi Vseros. konf., Otechestvo, Kazan, 2012, 90–94

[6] Karchevskii M. M., Fedotov A. E., “Ob odnom variante smeshannogo metoda konechnykh elementov dlya kvazilineinykh ellipticheskikh uravnenii”, Issled. po prikl. matem. i informatike, 24, Kazan. gos. un-t, Kazan, 2003, 74–80

[7] Karchevsky M. M., Fedotov A. E., “Error estimates and iterative procedure for mixed finite element solution of second-order quasi-linear elliptic problems”, Comput. Meth. Appl. Math., 4:4 (2004), 445–463 | DOI | Zbl

[8] Gogin A. P., Karchevskii M. M., “Ob odnom iteratsionnom metode dlya smeshannykh skhem konechnykh elementov”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 4, 2011, 5–10

[9] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972, 588 pp.

[10] Badriev I. B., Karchevskii M. M., “Convergence of an iterative process in a Banach space”, J. Math. Sci., 71:6 (1994), 2727–2735 | DOI | Zbl

[11] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980, 512 pp.

[12] Brezzi F., Fortin M., Mixed and Hybrid Finite Element Methods, Springer-Verlag, N. Y., 1991, 362 pp. | Zbl

[13] Temam R., Uravneniya Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981, 408 pp. | Zbl

[14] Farhloul M., “A mixed finite element method for a nonlinear Dirichlet problem”, IMA J. Numer. Anal., 18:1 (1998), 121–132 | DOI | Zbl

[15] Farhloul M., Manouzi H., “On a mixed finite element method for the $p$-Laplacian”, Can. Appl. Math. Quart., 8:1, 67–78 | Zbl

[16] Gaevskii Kh., Grëger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978, 336 pp.

[17] Vainberg M. M., Variatsionnye metody issledovaniya nelineinykh operatorov, Gos. izd-vo tekhn.-teoret. lit., M., 1956, 345 pp. | Zbl