On the nonconformal finite element method for the Stokes problem with a discontinuous coefficient
Sibirskij žurnal industrialʹnoj matematiki, Tome 10 (2007) no. 4, pp. 104-117.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{SJIM_2007_10_4_a10,
     author = {A. V. Rukavishnikov and V. A. Rukavishnikov},
     title = {On the nonconformal finite element method for the {Stokes} problem with a discontinuous coefficient},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {104--117},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2007_10_4_a10/}
}
TY  - JOUR
AU  - A. V. Rukavishnikov
AU  - V. A. Rukavishnikov
TI  - On the nonconformal finite element method for the Stokes problem with a discontinuous coefficient
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2007
SP  - 104
EP  - 117
VL  - 10
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2007_10_4_a10/
LA  - ru
ID  - SJIM_2007_10_4_a10
ER  - 
%0 Journal Article
%A A. V. Rukavishnikov
%A V. A. Rukavishnikov
%T On the nonconformal finite element method for the Stokes problem with a discontinuous coefficient
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2007
%P 104-117
%V 10
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2007_10_4_a10/
%G ru
%F SJIM_2007_10_4_a10
A. V. Rukavishnikov; V. A. Rukavishnikov. On the nonconformal finite element method for the Stokes problem with a discontinuous coefficient. Sibirskij žurnal industrialʹnoj matematiki, Tome 10 (2007) no. 4, pp. 104-117. http://geodesic.mathdoc.fr/item/SJIM_2007_10_4_a10/

[1] Crouzeix M., Raviart P. A., “Comforming and non-conforming finite element methods for solving the stationary Stokes equations”, RAIRO Anal. Numer., 7 (1973), 33–76 | MR

[2] Brezzi F., Fortin M., Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991 | MR | Zbl

[3] Rukavishnikov A. V., “Chislennyi metod resheniya zadachi Stoksa s razryvnym koeffitsientom”, Vychisl. metody i programmirovanie, 6:1 (2005), 21–30

[4] Bernardi C., Maday Y., Patera A., “A new nonconforming approach to domain decomposition: the mortar element method”, Nonlinear Partial Differential Equations and their Applications, Pitman, Paris, 1989, 13–51 | MR

[5] Braess D., Dahmen W., Wieners C., “A multigrid algorithm for the mortar finite element methods”, SIAM J. Numer. Anal., 37:1 (1999), 48–69 | DOI | MR | Zbl

[6] Wohlmuth B., “Hierarchical a posteriori error estimators for mortar finite element methods with Lagrange multipliers”, SIAM J. Numer. Anal., 36:5 (1999), 1636–1658 | DOI | MR | Zbl

[7] Ben Belgacem F., “The mixed mortar finite element method for the incompressible Stokes problem: convergence analysis”, SIAM J. Numer. Anal., 37:4 (2000), 1085–1100 | DOI | MR | Zbl

[8] Ben Belgacem F., “A stabilized domain decomposition method with nonmatching grids for the Stokes problem in three dimensions”, SIAM J. Numer. Anal., 42:2 (2004), 667–685 | DOI | MR | Zbl

[9] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980 | MR

[10] Rukavishnikov A. V., O differentsialnykh svoistvakh resheniya zadachi Stoksa s razryvnym koeffitsientom, Preprint, No 9, Khabarovsk. otd-nie In-ta prikladnoi matematiki DVO RAN, Vladivostok, 2004

[11] Kuznetsov Yu. A., “Efficient iterative solvers for elliptic finite elements problems on nonmatching grids”, Russian J. Numer. Anal. Math. Modelling, 10:3 (1995), 187–211 | MR | Zbl

[12] Braess D., Finite Elements: Theory, Fast solvers, and Applications in Solid Mechanics, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl

[13] Agouzal A., Thomas J.-P., “Une methode d'element finis hybrides en decomposition de domaines”, RAIRO Model. Math. Anal. Numer., 29 (1995), 749–764 | MR | Zbl

[14] Lions J.-L., Magenes E., Non-Homogeneous Boundary Value Problems and applications, Part I, Springer-Verlag, New York, 1972

[15] Boland J. M., Nicolaides R. A., “Stability of finite elements under divergence constraints”, SIAM J. Numer. Anal., 20:4 (1983), 722–731 | DOI | MR | Zbl