Analysis of the Schwarz algorithm for mixed finite elements methods
- Volume: 26, Issue: 6, page 739-756
- ISSN: 0764-583X
Access Full Article
topHow to cite
topEwing, R. E., and Wang, J.. "Analysis of the Schwarz algorithm for mixed finite elements methods." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 26.6 (1992): 739-756. <http://eudml.org/doc/193683>.
@article{Ewing1992,
author = {Ewing, R. E., Wang, J.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Schwarz alternating algorithm; domain decomposition; second-order elliptic differential equations; Neumann boundary conditions; Galerkin method; mixed finite element method; convergence},
language = {eng},
number = {6},
pages = {739-756},
publisher = {Dunod},
title = {Analysis of the Schwarz algorithm for mixed finite elements methods},
url = {http://eudml.org/doc/193683},
volume = {26},
year = {1992},
}
TY - JOUR
AU - Ewing, R. E.
AU - Wang, J.
TI - Analysis of the Schwarz algorithm for mixed finite elements methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1992
PB - Dunod
VL - 26
IS - 6
SP - 739
EP - 756
LA - eng
KW - Schwarz alternating algorithm; domain decomposition; second-order elliptic differential equations; Neumann boundary conditions; Galerkin method; mixed finite element method; convergence
UR - http://eudml.org/doc/193683
ER -
References
top- [1] I. BABUŠKA, The finite element method with Lagrangian multipliers, Numer. Math., 20 (1973), 179-192. Zbl0258.65108MR359352
- [2] I. BABUŠKA, On the Schwarz algorithm in the theory of differential equations of mathematical physics, Tchecosl. Math. J., 8 (1958), 328-342 (in Russian). Zbl0083.11301
- [3] J. H. BRAMBLE, R. E. EWING, J. E. PASCIAK and A. H. SCHATZ, A preconditioning technique for the efficient solution of problems with local grid refinement, Compt. Meth. Appl. Mech. Eng., 67 (1988), 149-159. Zbl0619.76113
- [4] J. H. BRAMBLE, J. E. PASCIAK, J. WANG and J. XU, Convergence estimates for product iterative methods with applications to domain decomposition and multigrid, Math. Comp. (to appear). Zbl0754.65085MR1090464
- [5] J. H. BRAMBLE, J. E. PASCIAK, J. WANG and J. XU, Convergence estimate for multigrid algorithms without regularity assumptions, Math. Comp. (to appear). Zbl0727.65101MR1079008
- [6] F. BREZZI, 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. Zbl0338.90047MR365287
- [7] F. BREZZI, J. Jr. DOUGLAS, R. DURÁN and L. D. MARINI, Mixed finite elements for second order elliptic problems in three variables, Numer. Math., 51 (1987), 237-250. Zbl0631.65107MR890035
- [8] F. BREZZI, J. Jr. DOUGLAS, R. FORTIN and L. D. MARINI, Efficient rectangular mixed finite elements in two and three space variables, R.A.I.R.O., Modél. Math. Anal. Numér., 21 (1987), 581-604. Zbl0689.65065MR921828
- [9] F. BREZZI, J. Jr. DOUGLAS and L. D. MARINI, Two families of mixed finite elements for second order elliptic problems, Numer. Math., 47 (1985), 217-235. Zbl0599.65072MR799685
- [10] J. Jr. DOUGLAS and J.E. ROBERTS, Global estimates for mixed finite element methods for second order elliptic equations, Math. Comp., 45 (1985), 39-52. Zbl0624.65109MR771029
- [11] J. Jr. DOUGLAS and J. WANG, Superconvergence of mixed finite element methods on rectangular domains, Calcolo, 26 (1989), 121-134. Zbl0714.65084MR1083049
- [12] J. Jr. DOUGLAS and J. WANG, A new family of mixed finite element spaces over rectangles, submitted. Zbl0806.65109MR1288240
- [13] R. E. EWING and J. WANG, Analysis of mixed finite element methods on locally-refined grids, submitted. Zbl0772.65071
- [14] R. E. EWING and J. WANG, Analysis of multilevel decomposition iterative methods for mixed finite element methods, submitted to R.A.I.R.O., Modél. Math. Anal. Numér. Zbl0823.65035
- [15] P. G. CIARLET, « The Finite Element Method for Elliptic Problems », North-Holland, New York, 1978. Zbl0383.65058MR520174
- [16] M. DRYJA and O. WIDLUND, An additive variant of the Schwarz alternating method for the case of many subregions, Technical Report, Courant Institute of Mathematical Sciences, 339 (1987).
- [17] M. DRYJA and O. WIDLUND, Some domain decomposition algorithms for elliptic problems, Technical Report, Courant Institute of Mathematical Sciences, 438 (1989). Zbl0719.65084MR1038100
- [18] R. FALK and J. OSBORN, Error estimates for mixed methods, R.A.I.R.O.,Modél. Math. Anal. Numér., 14 (1980), 249-277. Zbl0467.65062MR592753
- [19] M. FORTIN, An analysis of the convergence of mixed finite element methods, R.A.I.R.O., Modél. Math. Anal. Numér, 11 (1977), 341-354. Zbl0373.65055MR464543
- [20] R. GLOWINSKI and M. F. WHEELER, 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. Zbl0661.65105MR972509
- [21] P. L. LIONS, 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. Zbl0658.65090MR972510
- [22] T. P. MATHEW, « Domain Decomposition and Iterative Refinement Methods for Mixed Finite Element Discretizations of Elliptic Problems», Ph. D. Thesis, New York University, 1989.
- [23] A. M. MATSOKIN and S. V. NEPOMNYASCHIKH, A Schwarz alternating method in a subspace, Soviet Math., 29(10) (1985), 78-84. Zbl0611.35017
- [24] P.-A. RAVIART and J.-M. THOMAS, 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. Zbl0362.65089MR483555
- [25] H. A. SCHWARZ, Über einige Abbildungsaufgaben, Ges. Math. Abh., 11(1869), 65-83.
- [26] J. WANG, Convergence analysis without regularity assumptions for multigrid algorithme based on SOR smoothing, SIAM J. Numer. Anal, (to appear). Zbl0753.65093MR1173181
- [27] J. WANG, 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. Zbl0785.65115MR1159720
- [28] J. WANG, Convergence analysis of Schwarz algorithm and multilevel decomposition iterative methods II : non-self adjoint and indefinite elliptic problems, SIAM J. Numer. Anal, (submitted). Zbl0777.65066
- [29] J. WANG, Asymptotic expansions and L∞-error estimates for mixed finite element methods for second order elliptic problems, Numer. Math., 55 (1989), 401-430. Zbl0676.65109MR997230
Citations in EuDML Documents
top- Bedřich Sousedík, On adaptive BDDC for the flow in heterogeneous porous media
- R. E. Ewing, J. Wang, Analysis of multilevel decomposition iterative methods for mixed finite element methods
- Ronald H.W. Hoppe, Barbara Wohlmuth, Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.