How to avoid the use of Green's theorem in the Ciarlet-Raviart theory of variational crimes

Alexander Ženíšek

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1987)

  • Volume: 21, Issue: 1, page 171-191
  • ISSN: 0764-583X

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Ženíšek, Alexander. "How to avoid the use of Green's theorem in the Ciarlet-Raviart theory of variational crimes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 21.1 (1987): 171-191. <http://eudml.org/doc/193495>.

@article{Ženíšek1987,
author = {Ženíšek, Alexander},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Ciarlet-Raviart theory; variational problem; Green's theorem; discrete approximation; variational crimes; convergence; errors},
language = {eng},
number = {1},
pages = {171-191},
publisher = {Dunod},
title = {How to avoid the use of Green's theorem in the Ciarlet-Raviart theory of variational crimes},
url = {http://eudml.org/doc/193495},
volume = {21},
year = {1987},
}

TY - JOUR
AU - Ženíšek, Alexander
TI - How to avoid the use of Green's theorem in the Ciarlet-Raviart theory of variational crimes
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1987
PB - Dunod
VL - 21
IS - 1
SP - 171
EP - 191
LA - eng
KW - Ciarlet-Raviart theory; variational problem; Green's theorem; discrete approximation; variational crimes; convergence; errors
UR - http://eudml.org/doc/193495
ER -

References

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  1. [1] P. G. CIARLET, P. A. RAVIART, The combined effect of curved boundaries and numerical integration in isoparametric finite element methods. In : The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, Editor), Academic Press, New York, 1972, pp. 409-474. Zbl0262.65070MR421108
  2. [2] P. G. CIARLET, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978. Zbl0383.65058MR520174
  3. [3] P. DOKTOR, On the density of smooth functions in certain subspaces of Sobolev space. Commentationes Mathematicae Universitatis Carolinae 14 (1973), 609-622. Zbl0268.46036MR336317
  4. [4] 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, Editor), Academic Press, New York, 1972, pp. 689-710. Zbl0264.65068MR413554
  5. [5] G. STRANG, G. FIX, An Analysis of the Finite Element Method. Prentice-Hall Inc., Englewood Cliffs, N. J., 1973. Zbl0356.65096MR443377
  6. [6] M. ZLAMAL, The finite element method in domains with curved boundaries. Int. J. Numer. Meth. Engng. 5 (1973), 367-373. Zbl0254.65073MR395262
  7. [7] M. ZLAMAL, Curved elements in the finite element method. I. SIAM J. Numer. nal. 10 (1973), 229-240. Zbl0285.65067MR395263
  8. [8] A. ZENISEK, Curved triangular finite Cm-elements. Api. Mat. 23 (1978), 346-377. Zbl0404.35041MR502072
  9. [9] A. ZENISEK, Discrete forms of Friedrichs' inequalities in the finite element method. R.A.I.R.O. Anal. num. 15 (1981), 265-286. Zbl0475.65072MR631681
  10. [10] A. ZENISEK, Nonhomogeneous boundary conditions and curved triangular finite elements. Apl. Mat. (1981), 121-141. Zbl0475.65073MR612669

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