Analysis of mixed methods using conforming and nonconforming finite element methods

Zhangxin Chen

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1993)

  • Volume: 27, Issue: 1, page 9-34
  • ISSN: 0764-583X

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Chen, Zhangxin. "Analysis of mixed methods using conforming and nonconforming finite element methods." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 27.1 (1993): 9-34. <http://eudml.org/doc/193697>.

@article{Chen1993,
author = {Chen, Zhangxin},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {conforming; nonconforming; error estimates; mixed finite element methods; second order elliptic problems; variable coefficients},
language = {eng},
number = {1},
pages = {9-34},
publisher = {Dunod},
title = {Analysis of mixed methods using conforming and nonconforming finite element methods},
url = {http://eudml.org/doc/193697},
volume = {27},
year = {1993},
}

TY - JOUR
AU - Chen, Zhangxin
TI - Analysis of mixed methods using conforming and nonconforming finite element methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1993
PB - Dunod
VL - 27
IS - 1
SP - 9
EP - 34
LA - eng
KW - conforming; nonconforming; error estimates; mixed finite element methods; second order elliptic problems; variable coefficients
UR - http://eudml.org/doc/193697
ER -

References

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  1. [1] T. ARBOGAST, A new formulation of mixed finite element methods for second order elliptic problems (to appear). Zbl1248.65119
  2. [2] D. N. ARNOLD and F. BREZZI, Mixed and nonconforming finite element methods : implementation postprocessing and error estimates, RAIRO Model. Math. Anal Numér., 19 (1985), pp 7-32. Zbl0567.65078MR813687
  3. [3] F. BREZZI, J. DOUGLAS Jr and L. DONATELLA MARINI, Two families of mixed finite elements for second order elliptic problems, Numer Math., 47 (1985), pp 217-235. Zbl0599.65072MR799685
  4. [4] Z. CHEN, On the relationship between mixed and Galerkin finite element methods, Ph. D. thesis, Purdue University, West Lafayette, Indiana, August (1991). 
  5. [5] F. BREZZI and M. FORTIN, Hybrid and Mixed Finite Element Methods, to appear. Zbl0788.73002
  6. [6] P. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. Zbl0383.65058MR520174
  7. [7] J. DOUGLAS Jr and J. E. ROBERTS, Global estimates for mixed methods for second order elliptic problems, Math. Comp., 45 (1985), pp 39-52. Zbl0624.65109MR771029
  8. [8] R. FALK and J. OSBORN, Error estimates for mixed methods, RAIRO, Model. Math. Anal. Numér., 14 (1980), pp 249-277. Zbl0467.65062MR592753
  9. [9] M. FORTIN and M. SOULIE, A non-conforming piecewise quadratic finite element on triangles, Internat. J. Numer. Methods Engrg., 19 (1983), pp 505-520. Zbl0514.73068MR702056
  10. [10] B. X. FRAEIJS DE VEUBEKE, Displacement and equilibrium models in the finite element method, in Stress Analysis, O. C. Zienkiewicz and G. Hohste (eds.), John Wiley, New York, 1965. Zbl0359.73007
  11. [11] L. DONATELLA MARINI, An inexpensive method for the evaluation of the solution of the lowest order Raviart-Thomas mixed method, SIAM J. Numer. Anal., 22 (1985), pp 493-496. Zbl0573.65082MR787572
  12. [12] L. DONATELLA MARINI and P. PIETRA, An abstract theory for mixed approximations of second order elliptic problems, Mat. Apl. Comput., 8 (1989), pp 219-239. Zbl0711.65091MR1067287
  13. [13] P. A. RAVIART and J. M. THOMAS, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of the Finite Element Method, Lecture Notes in Math. 606, Springer-Verlag, Berlin and New York (1977), pp 292-315. Zbl0362.65089MR483555

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