@article{M2AN_1999__33_4_747_0, author = {Douglas, Jim Jr. and Santos, Juan E. and Sheen, Dongwoo and Ye, Xiu}, title = {Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {33}, year = {1999}, pages = {747-770}, mrnumber = {1726483}, zbl = {0941.65115}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_1999__33_4_747_0} }
Douglas, Jim Jr.; Santos, Juan E.; Sheen, Dongwoo; Ye, Xiu. Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 33 (1999) pp. 747-770. http://gdmltest.u-ga.fr/item/M2AN_1999__33_4_747_0/
[1] Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates. RAIRO Model. Math. Anal. Numér. 19 (1985) 7-32. | Numdam | MR 813687 | Zbl 0567.65078
and ,[2] Approximation of Elliptic Boundary-Value Problems. Wiley-Interscience, New York (1972). | MR 478662 | Zbl 0248.65063
,[3] The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994). | MR 1278258 | Zbl 0804.65101
and ,[4] The Finite Element Method for Elliptic Equations. North-Holland, Amsterdam (1978). | MR 520174
.[5] Conforming and nonconforming finite element methods for solving the stationary Stokes equations. RAIRO Anal. Numér. (déc. 1973) 33-75. | Numdam | MR 343661 | Zbl 0302.65087
and ,[6] Methodes de décomposition de domaines pour les problèmes de propagation d'ondes en régime harmonique. Ph.D. thesis, University of Paris IX Dauphine, France (1991). | Zbl 0849.65085
,[7] A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods. Numer. Math. 65 (1993) 95-108. | MR 1217441 | Zbl 0813.65122
, , and ,[8] Some non-conforming finite elements for the plate bending problem. RAIRO Anal. Numér. 9 (1975) 9-53. | Numdam | MR 423968 | Zbl 0319.73042
and ,[9] On the Schwarz alternating method, in Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, G. Golub, G. Meurant and J. Periaux Eds. SIAM, Philadelphia (1988) 1-42. | MR 972510 | Zbl 0658.65090
.[10] On the Schwarz alternating method III: a variant for nonoverlapping subdomains, in Domain Decomposition Methods for Partial Differential Equations, T.F. Chan, R. Glowinski, J. Periaux and O. B. Widlund Eds., SIAM, Philadelphia (1990) 202-223. | MR 1064345 | Zbl 0704.65090
.[11] Simple nonconforming quadrilatéral Stokes element. Numer. Methods Partial Differential Equations 8 (1992) 97-111. | MR 1148797 | Zbl 0742.76051
and ,[12] Variational crimes in the finite element method, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A.K. Aziz Ed., Academie Press, New York (1972) 689-710. | MR 413554 | Zbl 0264.65068
,[13] An Analysis of the Finite Element Method. Prentice-Hall, Englewood Cliffs (1973). | MR 443377 | Zbl 0356.65096
and ,