no. 6
A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations
ESAIM: Modélisation mathématique et analyse numérique, Tome 26 (1992) no. 6, pp. 673-708. 
@article{M2AN_1992__26_6_673_0,
     author = {Lu, T. and Neittaanmaki, P. and Tai, X.-C.},
     title = {A parallel splitting-up method for partial differential equations and its applications to {Navier-Stokes} equations},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {673--708},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {26},
     number = {6},
     year = {1992},
     mrnumber = {1183413},
     zbl = {0756.65129},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1992__26_6_673_0/}
}
TY  - JOUR
AU  - Lu, T.
AU  - Neittaanmaki, P.
AU  - Tai, X.-C.
TI  - A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1992
SP  - 673
EP  - 708
VL  - 26
IS  - 6
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1992__26_6_673_0/
LA  - en
ID  - M2AN_1992__26_6_673_0
ER  - 
%0 Journal Article
%A Lu, T.
%A Neittaanmaki, P.
%A Tai, X.-C.
%T A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1992
%P 673-708
%V 26
%N 6
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1992__26_6_673_0/
%G en
%F M2AN_1992__26_6_673_0
Lu, T.; Neittaanmaki, P.; Tai, X.-C. A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 26 (1992) no. 6, pp. 673-708. http://www.numdam.org/item/M2AN_1992__26_6_673_0/

[1] A. J. Chorin, Numerical solution of Navier-Stokes equations Math. Comp., 22 (1968), 745-762. | MR | Zbl

[2]C. Cuvelier, A. Segal, A. A. Van Steenhoven, Finite element methods and Navier-Stokes equations, D. Reidel Publishing Company, 1986. | MR | Zbl

[3] J. Douglas and H. Rachford, On the numencal solution of the heat conduction problem in two and three space variables, Trans. Amer. Math. Soc., 82 2 (1956), 421-439. | MR | Zbl

[4] G. Girault and P.-A. Raviart, Finite element methods for Navier-Stokes equations, Theory and algorithms, Springer-Verlag, Berlin, 1986. | MR | Zbl

[5] A. R. Gourlay, Splitting-up methods for time dependent partial differential equations, in The state of the art in numerical analysis (proc. Conf. Univ. York, Heslington, 1976), Academic Press, London, 1977, pp. 757-796. | MR

[6] J. G. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier Stokes problem : I. Regularity of the solution and second-order error estimates for the spatial discretization, SIAM J. Numer. Anal., 19 (1982), 275-311. | MR | Zbl

[7] M. Křižek and P. Neittaanmäki, Finite element approximation to variational problems with applications, Pitman Monographs in Pure and Applied Mathematics 50, Longman, 1990. | MR | Zbl

[8] O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York, Second Edition, 1969. | MR | Zbl

[9] O. A. Ladyzhenskaya and V. I. Rivkind, On the alternating method for the computation of a viscous incompressible fluid flow in cylindrical coordinates, Izv. Akad. Nauk, 35 (1971), 251-268. | MR | Zbl

[10] J. L. Lions and R. Temam, Éclatement et décentralisation en calcul des variations, in « Proc. of Symposium on Optimization », Lecture Notes in Mathematics, Vol. 132, Springer Verlag, 1970, pp. 196-217. | MR | Zbl

[11] T. Lu, P. Neittaanmäki and X.-C. Tai, A parallel spliting-up method and its application to Naver-Stokes equations, Appl. Math. Lett., 4 (1989). 25-29. | MR | Zbl

[12] G. I. Marchuk, Methods of numerical mathematics, Springer-Verlag, 1982. | MR | Zbl

[13] D. W. Peaceman and H. H. Rachford, The numerical solution of parabolic and elliptic differential equations, SIAM, 3 (1955), 28-42. | MR | Zbl

[14] J. Shen, On error estimates of projection methods for Navier-Stokes equations : First order schemes, To appear in SIAM J. Numer. Anal. | MR | Zbl

[15] X. C. Tai and P. Neittaanmäki, A parallel finite element splitting up method for parabolic problems, Numerical methods for partial differential equations, 7 (1991), 209-225. | MR | Zbl

[16] R. Temam Sur l'approximation de la solution des équations de Navier-Stokes par la méthode de pas fractionnaires (I), Arch. Rational Mech. Anal., 32 (1969), 135-153. | MR | Zbl

[17] R. Temam, Numerical analysis, D. Reidel Publishing Company, Dordrecht, North-Holland, 1973. | MR | Zbl

[18] R. Temam Navier-Stokes equations, North-Holland, 1977. | MR | Zbl

[19] N. N. Yanenko, The method of fractional steps for solving multi-dimensional problems of mathematical physics, Novosibirsk, Nauka, 1967. | Zbl

[20] L. Ying, Viscosity splitting method for three dimensional Navier-Stokes equations, Acta Math. Sinica New Series, No. 3, 4 (1988), 210-226. | MR | Zbl