@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: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {479--499}, publisher = {Elsevier}, volume = {32}, number = {4}, year = {1998}, mrnumber = {1636376}, zbl = {0910.65079}, language = {en}, url = {http://www.numdam.org/item/M2AN_1998__32_4_479_0/} }
TY - JOUR AU - Chen, Zhangxin TI - Expanded mixed finite element methods for linear second-order elliptic problems, I JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1998 SP - 479 EP - 499 VL - 32 IS - 4 PB - Elsevier UR - http://www.numdam.org/item/M2AN_1998__32_4_479_0/ LA - en ID - M2AN_1998__32_4_479_0 ER -
%0 Journal Article %A Chen, Zhangxin %T Expanded mixed finite element methods for linear second-order elliptic problems, I %J ESAIM: Modélisation mathématique et analyse numérique %D 1998 %P 479-499 %V 32 %N 4 %I Elsevier %U http://www.numdam.org/item/M2AN_1998__32_4_479_0/ %G en %F M2AN_1998__32_4_479_0
Chen, Zhangxin. Expanded mixed finite element methods for linear second-order elliptic problems, I. ESAIM: Modélisation mathématique et analyse numérique, Volume 32 (1998) no. 4, pp. 479-499. http://www.numdam.org/item/M2AN_1998__32_4_479_0/
[1] On the implementation of mixed methods as nonconforming methods for second order elliptic problems, Math. Comp. 64 (1995), 943-972. | MR | Zbl
and ,[2] Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates, RAIRO Modèl. Math. Anal. Numér. 19 (1985), 7-32. | EuDML | Numdam | MR | Zbl
and ,[3] A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems, Math. Comp. 50 (1988), 1-17. | MR | Zbl
and ,[4] Mixed finite elements for second order elliptic problems in three variables, Numer. Math. 51 (1987), 237-250. | EuDML | MR | Zbl
, , and ,[5] Efficient rectangular mixed finite elements in two and three space variables, RAIRO Modèl. Math. Anal. Numér. 21 (1987), 581-604. | EuDML | Numdam | MR | Zbl
, , and ,[6] Two families of mixed finite elements for second order elliptic problems, Numer. Math. 47 (1985), 217-235. | EuDML | MR | Zbl
, and ,[7] Conjugate gradient methods for partial differential equations, Report 129, Computer Science Department, Yale University, New Haven, CT (1978).
,[8] Two-phase unsaturated flow. one dimensional simulation and air phase velocities, Water Resources Research 28 (1992), 2819-2828.
and ,[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 | Zbl
,[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 | Zbl
,[12] BDM mixed methods for a nonlinear elliptic problem, J. Comp. Appl. Math. 53 (1994), 207-223. | MR | Zbl
,[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 | Zbl
,[14] Prismatic mixed finite elements for second order elliptic problems, Calcolo 26 (1989), 135-148. | MR | Zbl
and ,[15] 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 | Zbl
, and ,[16] 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 | Zbl
, and ,[17] The approximation of the pressure by a mixed method in the simulation of miscible displacement, RAIRO Anal. Numér. 17 (1983), 17-33. | Numdam | MR | Zbl
, and ,[18] 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 | Zbl
, and ,[19] 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.
and ,[20] Global estimates for mixed methods for second order elliptic problems, Math. Comp.. 45 (1985), 39-52. | MR | Zbl
and ,[21] A new family of mixed finite element spaces over rectangles, Mat. Aplic. Comput. 12 (1993), 183-197. | MR | Zbl
and ,[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 | Zbl
,[23] 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 | Zbl
, and ,[24] A new mixed finite element method for the Timoshenko beam problem, RAIRO Mod. Math. Anal. Numér. 25 (1991), 561-578. | Numdam | MR | Zbl
and ,[25] Optimal L∞-error estimates for nonconforming and mixed finite element methods of lowest order, Numer. Math. 50 (1987), 587-611. | MR | Zbl
and ,[26] Elliptic Partial Differential Equations of Second Order, Grundlehren der Mathematischen Wissenschaften, vol. 224, Springer Verlag, Berlin, 1977. | MR | Zbl
and ,[27] Mixed finite elements in R3, Numer. Math. 35 (1980) 315-341. | MR | Zbl
,[28] A new family of mixed finite elements in R3, Numer. Math. 50 (1986), 57- 81. | MR | Zbl
,[29] Solution of sparse indefinite systems of linear equations, SIAM Numer. anal. 12 (1975), 617-629. | MR | Zbl
and ,[30] A mixed finite element method for second order elliptic problems, Lecture Notes in Math. 606, Springer, Berlin, 1977, pp. 292-315. | MR | Zbl
and ,[31] A preconditioned iterative method for saddle point problems, SIAM J. Matrix Anal. Appl. 13 (1992), 887-904. | MR | Zbl
and ,[32] Postprocessing schemes for some mixed finite elements, RAIRO Modèl. Math. Anal. Numér. 25 (1991), 151-167. | Numdam | MR | Zbl
,[33] Experimental and numencal analysis of two phase infiltration in a partially saturated soil, Transport in Porous Media 1 (1986), 27-55.
and ,