@article{M2AN_1992__26_6_739_0, author = {Ewing, R. E. and Wang, J.}, title = {Analysis of the {Schwarz} algorithm for mixed finite elements methods}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {739--756}, publisher = {AFCET - Gauthier-Villars}, address = {Paris}, volume = {26}, number = {6}, year = {1992}, mrnumber = {1183415}, zbl = {0765.65104}, language = {en}, url = {http://archive.numdam.org/item/M2AN_1992__26_6_739_0/} }
TY - JOUR AU - Ewing, R. E. AU - Wang, J. TI - Analysis of the Schwarz algorithm for mixed finite elements methods JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1992 SP - 739 EP - 756 VL - 26 IS - 6 PB - AFCET - Gauthier-Villars PP - Paris UR - http://archive.numdam.org/item/M2AN_1992__26_6_739_0/ LA - en ID - M2AN_1992__26_6_739_0 ER -
%0 Journal Article %A Ewing, R. E. %A Wang, J. %T Analysis of the Schwarz algorithm for mixed finite elements methods %J ESAIM: Modélisation mathématique et analyse numérique %D 1992 %P 739-756 %V 26 %N 6 %I AFCET - Gauthier-Villars %C Paris %U http://archive.numdam.org/item/M2AN_1992__26_6_739_0/ %G en %F M2AN_1992__26_6_739_0
Ewing, R. E.; Wang, J. Analysis of the Schwarz algorithm for mixed finite elements methods. ESAIM: Modélisation mathématique et analyse numérique, Tome 26 (1992) no. 6, pp. 739-756. http://archive.numdam.org/item/M2AN_1992__26_6_739_0/
[1] The finite element method with Lagrangian multipliers, Numer. Math., 20 (1973), 179-192. | MR | Zbl
,[2] On the Schwarz algorithm in the theory of differential equations of mathematical physics, Tchecosl. Math. J., 8 (1958), 328-342 (in Russian). | Zbl
,[3] A preconditioning technique for the efficient solution of problems with local grid refinement, Compt. Meth. Appl. Mech. Eng., 67 (1988), 149-159. | Zbl
, , and ,[4] Convergence estimates for product iterative methods with applications to domain decomposition and multigrid, Math. Comp. (to appear). | MR | Zbl
, , and ,[5] Convergence estimate for multigrid algorithms without regularity assumptions, Math. Comp. (to appear). | MR | Zbl
, , and ,[6] On the existence, uniqueness, and approximation of saddle point problems arising from Lagrangian multipliers, R.A.I.R.O., Modél. Math. Anal. Numér., 2 (1974), 129-151. | Numdam | MR | Zbl
,[7] Mixed finite elements for second order elliptic problems in three variables, Numer. Math., 51 (1987), 237-250. | MR | Zbl
, , and ,[8] Efficient rectangular mixed finite elements in two and three space variables, R.A.I.R.O., Modél. Math. Anal. Numér., 21 (1987), 581-604. | Numdam | MR | Zbl
, , and ,[9] Two families of mixed finite elements for second order elliptic problems, Numer. Math., 47 (1985), 217-235. | MR | Zbl
, and ,[10] Global estimates for mixed finite element methods for second order elliptic equations, Math. Comp., 45 (1985), 39-52. | MR | Zbl
and ,[11] Superconvergence of mixed finite element methods on rectangular domains, Calcolo, 26 (1989), 121-134. | MR | Zbl
and ,[12] A new family of mixed finite element spaces over rectangles, submitted. | MR | Zbl
and ,[13] Analysis of mixed finite element methods on locally-refined grids, submitted. | Zbl
and ,[14] Analysis of multilevel decomposition iterative methods for mixed finite element methods, submitted to R.A.I.R.O., Modél. Math. Anal. Numér. | Numdam | Zbl
and ,[15] The Finite Element Method for Elliptic Problems », North-Holland, New York, 1978. | MR | Zbl
, «[16] An additive variant of the Schwarz alternating method for the case of many subregions, Technical Report, Courant Institute of Mathematical Sciences, 339 (1987).
and ,[17] Some domain decomposition algorithms for elliptic problems, Technical Report, Courant Institute of Mathematical Sciences, 438 (1989). | MR
and ,[18] Error estimates for mixed methods, R.A.I.R.O.,Modél. Math. Anal. Numér., 14 (1980), 249-277. | Numdam | MR | Zbl
and ,[19] An analysis of the convergence of mixed finite element methods, R.A.I.R.O., Modél. Math. Anal. Numér, 11 (1977), 341-354. | Numdam | MR | Zbl
,[20] Domain decomposition and mixed finite element methods for elliptic problems, In the Proceedings of the First International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, G. H. Golub, G. A. Meurant and J. Périaux (eds.), 1988. | MR | Zbl
and ,[21] On the Schwarz alternating method, In the Proceedings of the First International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, G. H. Golub, G. A. Meurant and J. Périaux (eds.), 1988. | MR | Zbl
,[22] Domain Decomposition and Iterative Refinement Methods for Mixed Finite Element Discretizations of Elliptic Problems», Ph. D. Thesis, New York University, 1989.
, «[23] A Schwarz alternating method in a subspace, Soviet Math., 29(10) (1985), 78-84. | Zbl
and ,[24] A mixed finite element method for 2nd order elliptic problems, In Mathematical Aspects of Finite Element Methods, Lecture Notes in Math. (606), Springer-Verlag, Berlin and New York, 1977, 292-315. | MR | Zbl
and ,[25] Über einige Abbildungsaufgaben, Ges. Math. Abh., 11(1869), 65-83.
,[26] Convergence analysis without regularity assumptions for multigrid algorithme based on SOR smoothing, SIAM J. Numer. Anal, (to appear). | MR | Zbl
,[27] Convergence analysis of Schwarz algorithm and multilevel decomposition iterative methods I : self adjoint and positive definite elliptic problems, SIAM J. Numer. Anal, (submitted) and in the « Proceeding of International Conference on Iterative Methods in Linear Algebra », Belgium, 1991. | MR | Zbl
,[28] Convergence analysis of Schwarz algorithm and multilevel decomposition iterative methods II : non-self adjoint and indefinite elliptic problems, SIAM J. Numer. Anal, (submitted). | Zbl
,[29] Asymptotic expansions and L∞-error estimates for mixed finite element methods for second order elliptic problems, Numer. Math., 55 (1989), 401-430. | MR | Zbl
,