Geodesic
Numerical solution to a stokes interface problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 1, pp. 111-122 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A numerical algorithm is described for solving the generalized eigenvalue problem arising in the study of the spectrum of a preconditioned operator in the pressure equation derived from a Stokes interface problem. The algorithm is implemented for two finite element schemes. It is tested for a problem with an analytical solution and is applied to spectrum computations in the case of a piecewise constant viscosity. A large number of numerical experiments are analyzed, and recommendations are given for solving the Stokes interface problem in practice. 
@article{ZVMMF_2009_49_1_a7,
     author = {E. V. Chizhonkov},
     title = {Numerical solution to a stokes interface problem},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {111--122},
     year = {2009},
     volume = {49},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a7/}
}
TY  - JOUR
AU  - E. V. Chizhonkov
TI  - Numerical solution to a stokes interface problem
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 111
EP  - 122
VL  - 49
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a7/
LA  - ru
ID  - ZVMMF_2009_49_1_a7
ER  - 
%0 Journal Article
%A E. V. Chizhonkov
%T Numerical solution to a stokes interface problem
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 111-122
%V 49
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a7/
%G ru
%F ZVMMF_2009_49_1_a7
E. V. Chizhonkov. Numerical solution to a stokes interface problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 1, pp. 111-122. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a7/

[1] Brackbill J. U., Rothe D. B., Zemach C., “A continuum method for modeling surface tension”, J. Comput. Phys., 100 (1992), 335–354 | DOI | MR | Zbl

[2] Osher S., Fedkiw R. P., “Level set methods: An overview and some recent results”, J. Comput. Phys., 169 (2001), 463–502 | DOI | MR | Zbl

[3] Chen Z., Zou J., “Finite element method and its convergence for elliptic and parabolic interface problems”, Numer. Math., 79 (1998), 175–202 | DOI | MR | Zbl

[4] Plum M., Wieners C., “Optimal a priori estimates for interface problems”, Numer. Math., 95 (2003), 735–759 | DOI | MR | Zbl

[5] Bakhvalov H. S., “Effektivnye metody resheniya zhestkikh mnogomernykh mnogoparametricheskikh zadach”, Zh. vychisl. matem. i matem. fiz., 39:12 (1999), 2019–2049 | MR | Zbl

[6] Chizhonkov E. V., Relaksatsionnye metody resheniya sedlovykh zadach, IVM RAN, M., 2002

[7] Olshanskii M. A., Reusken A., “Analysis of a Stokes interface problem”, Numer. Math., 103 (2006), 129–149 | DOI | MR | Zbl

[8] Gunzburger M., Finite element methods for viscous incompressible flow: a guide to theory, practice and alghorithms, Acad. Press, Boston, 1989 | MR | Zbl

[9] Mikhlin S. G., “Spektr puchka operatorov teorii uprugosti”, Uspekhi matem. nauk, 28:3(171) (1973), 43–82 | Zbl

[10] Crouzeix M., “On an operator related to the convergence of Uzawa's algorithm for the Stokes equation”, Comput. Sci. for 21st Century, Wiley, Chichester, 1997, 242–249 | Zbl

[11] Aristov P. P., Chizhonkov E. V., On the constant in the LBB condition for rectangular domains, Rept no 9534, Dept. Math. Univ. Nijmegen, The Netherlands, Sept. 1995

[12] Dyakonov E. G., “Otsenki vychislitelnoi raboty dlya kraevykh zadach s operatorom Stoksa”, Izv. vuzov. Matematika, 1983, no. 7, 46–58 | MR

[13] Chizhonkov E. V., Olshanskii M. A., “On the domain geometry dependence of the LBB condition”, M2AN Math. Model. Numer. Anal., 34:5 (2000), 935–951 | DOI | MR | Zbl

[14] Babuska I., Osborn J., “Eigenvalue problems”, Handbook of Numer. Analys, Vol. II, Ciariet P. G. and Lions J. L., North Holland, 1991 | MR | Zbl

[15] Chizhonkov E. V., On the constant in the LBB condition for ring domains, Rept no 9537, Dept. Math. Univ. Nijmegen, The Netherlands, October 1995

[16] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR

[17] U. Kauell (red.), Zarubezhnye biblioteki i pakety programm po vychislitelnoi matematike, Nauka, M., 1993 | MR

[18] Khemming R. V., Chislennye metody dlya nauchnykh rabotnikov i inzhenerov, Nauka, M., 1972 | MR