Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 4, pp. 747-770.
@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: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {747--770},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {4},
     year = {1999},
     mrnumber = {1726483},
     zbl = {0941.65115},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1999__33_4_747_0/}
}
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Douglas, Jim Jr.; Santos, Juan E.; Sheen, Dongwoo; Ye, Xiu. Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 4, pp. 747-770. http://www.numdam.org/item/M2AN_1999__33_4_747_0/

[1] D.N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates. RAIRO Model. Math. Anal. Numér. 19 (1985) 7-32. | Numdam | MR | Zbl

[2] J.-P. Aubin, Approximation of Elliptic Boundary-Value Problems. Wiley-Interscience, New York (1972). | MR | Zbl

[3] S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994). | MR | Zbl

[4] P.G. Ciarlet. The Finite Element Method for Elliptic Equations. North-Holland, Amsterdam (1978). | MR

[5] M. Crouzeix and P.-A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations. RAIRO Anal. Numér. (déc. 1973) 33-75. | Numdam | MR | Zbl

[6] B. Després, 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

[7] J. Jr. Douglas, P.J. Paes Leme, J.E. Roberts and J. Wang, 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 | Zbl

[8] P. Lascaux and P. Lesaint, Some non-conforming finite elements for the plate bending problem. RAIRO Anal. Numér. 9 (1975) 9-53. | Numdam | MR | Zbl

[9] P.L. Lions. 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 | Zbl

[10] P.L. Lions. 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 | Zbl

[11] R. Rannacher and S. Turek, Simple nonconforming quadrilatéral Stokes element. Numer. Methods Partial Differential Equations 8 (1992) 97-111. | MR | Zbl

[12] G. Strang, 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 | Zbl

[13] G. Strang and G.J. Fix, An Analysis of the Finite Element Method. Prentice-Hall, Englewood Cliffs (1973). | MR | Zbl