Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems

Jim Jr. Douglas; Juan E. Santos; Dongwoo Sheen; Xiu Ye

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 4, page 747-770
  • ISSN: 0764-583X

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Douglas, Jim Jr., et al. "Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.4 (1999): 747-770. <http://eudml.org/doc/193944>.

@article{Douglas1999,
author = {Douglas, Jim Jr., Santos, Juan E., Sheen, Dongwoo, Ye, Xiu},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {quadrilateral elements; domain decomposition; iterative methods; nonconforming Galerkin methods; second order elliptic equations; error estimates},
language = {eng},
number = {4},
pages = {747-770},
publisher = {Dunod},
title = {Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems},
url = {http://eudml.org/doc/193944},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Douglas, Jim Jr.
AU - Santos, Juan E.
AU - Sheen, Dongwoo
AU - Ye, Xiu
TI - Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 4
SP - 747
EP - 770
LA - eng
KW - quadrilateral elements; domain decomposition; iterative methods; nonconforming Galerkin methods; second order elliptic equations; error estimates
UR - http://eudml.org/doc/193944
ER -

References

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  1. [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. Zbl0567.65078MR813687
  2. [2] J.-P. Aubin, Approximation of Elliptic Boundary-Value Problems. Wiley-Interscience, New York (1972). Zbl0248.65063MR478662
  3. [3] S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994). Zbl0804.65101MR1278258
  4. [4] P.G. Ciarlet. The Finite Element Method for Elliptic Equations. North-Holland, Amsterdam (1978). Zbl0383.65058MR520174
  5. [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. Zbl0302.65087MR343661
  6. [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). Zbl0849.65085
  7. [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. Zbl0813.65122MR1217441
  8. [8] P. Lascaux and P. Lesaint, Some non-conforming finite elements for the plate bending problem. RAIRO Anal. Numér. 9 (1975) 9-53. Zbl0319.73042MR423968
  9. [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. Zbl0658.65090MR972510
  10. [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. Zbl0704.65090MR1064345
  11. [11] R. Rannacher and S. Turek, Simple nonconforming quadrilatéral Stokes element. Numer. Methods Partial Differential Equations 8 (1992) 97-111. Zbl0742.76051MR1148797
  12. [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. Zbl0264.65068MR413554
  13. [13] G. Strang and G.J. Fix, An Analysis of the Finite Element Method. Prentice-Hall, Englewood Cliffs (1973). Zbl0356.65096MR443377

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