@article{M2AN_1998__32_4_479_0,
author = {Chen, Zhangxin},
title = {Expanded mixed finite element methods for linear second-order elliptic problems, I},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {32},
year = {1998},
pages = {479-499},
mrnumber = {1636376},
zbl = {0910.65079},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_1998__32_4_479_0}
}
Chen, Zhangxin. Expanded mixed finite element methods for linear second-order elliptic problems, I. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 32 (1998) pp. 479-499. http://gdmltest.u-ga.fr/item/M2AN_1998__32_4_479_0/
[1] and , On the implementation of mixed methods as nonconforming methods for second order elliptic problems, Math. Comp. 64 (1995), 943-972. | MR 1303084 | Zbl 0829.65127
[2] and , Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates, RAIRO Modèl. Math. Anal. Numér. 19 (1985), 7-32. | Numdam | MR 813687 | Zbl 0567.65078
[3] and , A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems, Math. Comp. 50 (1988), 1-17. | MR 917816 | Zbl 0643.65017
[4] , , and , Mixed finite elements for second order elliptic problems in three variables, Numer. Math. 51 (1987), 237-250. | MR 890035 | Zbl 0631.65107
[5] , , and , Efficient rectangular mixed finite elements in two and three space variables, RAIRO Modèl. Math. Anal. Numér. 21 (1987), 581-604. | Numdam | MR 921828 | Zbl 0689.65065
[6] , and , Two families of mixed finite elements for second order elliptic problems, Numer. Math. 47 (1985), 217-235. | MR 799685 | Zbl 0599.65072
[7] , Conjugate gradient methods for partial differential equations, Report 129, Computer Science Department, Yale University, New Haven, CT (1978).
[8] and , Two-phase unsaturated flow. one dimensional simulation and air phase velocities, Water Resources Research 28 (1992), 2819-2828.
[9] , Unified analysis of the hybrid form of mixed finite elements for second order elliptic problems, J. Engng. Math. 8 (1991), 91-102.
[10] , Analysis of mixed methods using conforming and nonconforming finite element methods, RAIRO Modèl. Math. Anal. Numér. 27 (1993), 9-34. | Numdam | MR 1204626 | Zbl 0784.65075
[11] , Lp-posteriori error analysis of mixed methods for linear and quasilinear elliptic problems, in Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations, I. Babuska et al., eds., The IMA Volumes in Mathematics and its Applications, Springer-Verlag, Berlin and New York, 75 (1995), 187-200. | MR 1370251 | Zbl 0831.65110
[12] , BDM mixed methods for a nonlinear elliptic problem, J. Comp. Appl. Math. 53 (1994), 207-223. | MR 1306126 | Zbl 0819.65129
[13] , Expanded mixed finite element methods for quasilinear second order elliptic problems II, IMA Prepnnt Series # 1278, 1994, RAIRO Modèl. Math. anal. Numér., in press. | Numdam | MR 1637069 | Zbl 0910.65080
[14] and , Prismatic mixed finite elements for second order elliptic problems, Calcolo 26 (1989), 135-148. | MR 1083050 | Zbl 0711.65089
[15] , and , Formulation of altemating-direction iterative methods for mixed methods in three space, in the Proceedings of the Simposium Internacional de Analisis Numérico, E. Ortiz, éd., Madrid (1987),21-30. | MR 899777 | Zbl 0609.65071
[16] , and , Alternating-direction iteration for mixed finite element methods, in the Proceedings of the Seventh International Conference on Computing Methods in Applied Sciences and Engineering VII, R. Glowinski and J. L. Lions, eds., North-Holland, December (1986). | MR 905295 | Zbl 0677.65105
[17] , and , The approximation of the pressure by a mixed method in the simulation of miscible displacement, RAIRO Anal. Numér. 17 (1983), 17-33. | Numdam | MR 695450 | Zbl 0516.76094
[18] , and , A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media, RAIRO Anal. Numér. 17 (1983), 249-265. | Numdam | MR 702137 | Zbl 0526.76094
[19] and , A description of some alternating-direction techniques for mixed finite element methods, in Mathematical and Computational Methods in Seismic Exploration and Reservoir Modeling, SIAM, Philadelphia, PA (1985), 37-53.
[20] and , Global estimates for mixed methods for second order elliptic problems, Math. Comp.. 45 (1985), 39-52. | MR 771029 | Zbl 0624.65109
[21] and , A new family of mixed finite element spaces over rectangles, Mat. Aplic. Comput. 12 (1993), 183-197. | MR 1288240 | Zbl 0806.65109
[22] , Error analysis in Lp, 1 ≤ p ≤ ∞, for mixed finite element methods for linear and quasi-linear elliptic problems, RAIRO Mod. Math. Anal. Numér. 22 (1988), 371-387. | Numdam | MR 958875 | Zbl 0698.65060
[23] , and , Preconditioning indefinite systems arising from the mixed finite element discretization of second order elliptic systems, in Preconditioned Conjugate Gradient Methods, O. Axelsson and L. Kolotilina, eds., Lecture Notes in Math. 1457, Springer-Verlag, Berlin (1990), 28-43. | MR 1101627 | Zbl 0719.65024
[24] and , A new mixed finite element method for the Timoshenko beam problem, RAIRO Mod. Math. Anal. Numér. 25 (1991), 561-578. | Numdam | MR 1111655 | Zbl 0779.73059
[25] and , Optimal L∞-error estimates for nonconforming and mixed finite element methods of lowest order, Numer. Math. 50 (1987), 587-611. | MR 880337 | Zbl 0597.65080
[26] and , Elliptic Partial Differential Equations of Second Order, Grundlehren der Mathematischen Wissenschaften, vol. 224, Springer Verlag, Berlin, 1977. | MR 473443 | Zbl 0361.35003
[27] , Mixed finite elements in R3, Numer. Math. 35 (1980) 315-341. | MR 592160 | Zbl 0419.65069
[28] , A new family of mixed finite elements in R3, Numer. Math. 50 (1986), 57- 81. | MR 864305 | Zbl 0625.65107
[29] and , Solution of sparse indefinite systems of linear equations, SIAM Numer. anal. 12 (1975), 617-629. | MR 383715 | Zbl 0319.65025
[30] and , A mixed finite element method for second order elliptic problems, Lecture Notes in Math. 606, Springer, Berlin, 1977, pp. 292-315. | MR 483555 | Zbl 0362.65089
[31] and , A preconditioned iterative method for saddle point problems, SIAM J. Matrix Anal. Appl. 13 (1992), 887-904. | MR 1168084 | Zbl 0760.65033
[32] , Postprocessing schemes for some mixed finite elements, RAIRO Modèl. Math. Anal. Numér. 25 (1991), 151-167. | Numdam | MR 1086845 | Zbl 0717.65081
[33] and , Experimental and numencal analysis of two phase infiltration in a partially saturated soil, Transport in Porous Media 1 (1986), 27-55.