no. 1
Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 1, pp. 89-97 
@article{M2AN_1999__33_1_89_0,
     author = {Zhou, Aihui},
     title = {Multi-parameter asymptotic error resolution of the mixed finite element method for the {Stokes} problem},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {89--97},
     year = {1999},
     publisher = {EDP Sciences},
     volume = {33},
     number = {1},
     mrnumber = {1685745},
     zbl = {0917.76042},
     language = {en},
     url = {https://www.numdam.org/item/M2AN_1999__33_1_89_0/}
}
TY  - JOUR
AU  - Zhou, Aihui
TI  - Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1999
SP  - 89
EP  - 97
VL  - 33
IS  - 1
PB  - EDP Sciences
UR  - https://www.numdam.org/item/M2AN_1999__33_1_89_0/
LA  - en
ID  - M2AN_1999__33_1_89_0
ER  - 
%0 Journal Article
%A Zhou, Aihui
%T Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1999
%P 89-97
%V 33
%N 1
%I EDP Sciences
%U https://www.numdam.org/item/M2AN_1999__33_1_89_0/
%G en
%F M2AN_1999__33_1_89_0
Zhou, Aihui. Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 1, pp. 89-97. https://www.numdam.org/item/M2AN_1999__33_1_89_0/

[1] I. Babuska, The finite element methods with Lagrangian multipliers. Numer. Math. 20 (1973) 179-192. | Zbl | MR

[2] C. Bernardi and G. Raugel, Analysis of some finite elements of the Stokes problem. Math. Comp. 44 (1985) 71-79. | Zbl | MR

[3] H. Blum, Asymptotic error expansion and defect correction in the finite element method Heidelberg (1990).

[4] F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. RAIRO Modèl. Math. Anal. Numer. 2 (1974) 129-151. | Zbl | MR | Numdam

[5] P. G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland(1978). | Zbl | MR

[6] R. Duran, R. H. Nochetto and J. Wang, Sharp maximum norm error estimates for finite element approximation for the Stokes problem in 2-d. Math. Comp. 51 (1988) 491-506. | Zbl | MR

[7] M. Fortin, Old and new éléments for incompressible flows.Int. J. Numer. Meth. Fluids 1 (1981) 347-367. | Zbl | MR

[8] V. Girault and P. A. Raviart, Finite Element Method for Navier-Stokes Equation, Theory and Algorithms. Springer-Verlag, Berlin and Heidelberg (1986). | Zbl | MR

[9] R.B. Kellogg and J.E. Osborn, A regularity result for the Stokes problem in a polygon. J. Func. Anal. 21 (1976) 397-413. | Zbl | MR

[10] Q. Lin, T. Lü and S. Shen, Asymptotic expansions for finite element approximations. Research Report IMS-11, Chengdu Branch of Academia Sinica (1983). | Zbl | MR

[11] Q. Lin, N. Yan and A. Zhou, A rectangle test for interpolated finite elements. in Proc. of Sys. Sci. & Sys. Eng. Great Wall (H.K.), Culture Publish Co. (1991), 217-229. | MR

[12] Q. Lin and Q. Zhu, The Preprocessing and Postprocessing for the Finite Element Method. Shanghai Scientïfic & Technical Publishers (1994) (in Chinese).

[13] G. Marchuk and V. Shaidurov, Difference Methods and their Extrapolation. Springer, New York (1983). | Zbl | MR

[14] R. Rannacher, Extrapolation techniques in the finite element method (A Survey). in Proc. of the Summer School in Numer. Anal Helsinki (1988).

[15] R. Teman, Navier-Stokes Equations North-Holland, Amsterdam (1979). | Zbl

[16] R. Verfürth, Error estimates for a mixed finite element approximation of the Stokes equations. RAIRO Modèl. Math. Anal. Num. 18 (1984) 175-182. | Zbl | MR | Numdam

[17] A. Zhou, Global superconvergence approximations of the mixed finite element method for the Stokes problem and the linearelasticity equation. RAIRO Modèl. Math. Anal. Num. 30, 4 (1996), 401-411. | Zbl | MR | Numdam

[18] A. Zhou and J. Li, The full approximation accuracy for the stream function-vorticity-pressure method. Numer. Math. 68 (1994) 427-435. | Zbl | MR

[19] A. Zhou, C. B. Liem and T. M. Shih, A parallel algorithm based on multi-parameter asymptotic error expansion, in Proc. of Conference on Scientific Computing, Hong Kong (1994).

[20] A. Zhou, C.B. Liem, T.M. Shih and T. Lu, A parallel muiti-parameter asymptotic error expansion and a parallel algorithm. Research Report IMS-61, Inst. Math. Sci., Academia Sinica (1994), see also Sys. Sci. & Math Scis. 10, 3 (1997). 253-260. | Zbl | MR