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, Volume 21 (1987) no. 1, p. 171-191
@article{M2AN_1987__21_1_171_0,
author = {\v Zen\'\i \v sek, Alexander},
title = {How to avoid the use of Green's theorem in the Ciarlet-Raviart theory of variational crimes},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {Dunod},
volume = {21},
number = {1},
year = {1987},
pages = {171-191},
zbl = {0623.65072},
mrnumber = {882690},
language = {en},
url = {http://www.numdam.org/item/M2AN_1987__21_1_171_0}
}

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, Volume 21 (1987) no. 1, pp. 171-191. http://www.numdam.org/item/M2AN_1987__21_1_171_0/

[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. | MR 421108 | Zbl 0262.65070

[2] P. G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978. | MR 520174 | Zbl 0383.65058

[3] P. Doktor, On the density of smooth functions in certain subspaces of Sobolev space. Commentationes Mathematicae Universitatis Carolinae 14 (1973), 609-622. | MR 336317 | Zbl 0268.46036

[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. | MR 413554 | Zbl 0264.65068

[5] G. Strang, G. Fix, An Analysis of the Finite Element Method. Prentice-Hall Inc., Englewood Cliffs, N. J., 1973. | MR 443377 | Zbl 0356.65096

[6] M. Zlamal, The finite element method in domains with curved boundaries. Int. J. Numer. Meth. Engng. 5 (1973), 367-373. | MR 395262 | Zbl 0254.65073

[7] M. Zlamal, Curved elements in the finite element method. I. SIAM J. Numer. nal. 10 (1973), 229-240. | MR 395263 | Zbl 0285.65067

[8] A. Zenisek, Curved triangular finite Cm-elements. Api. Mat. 23 (1978), 346-377. | MR 502072 | Zbl 0404.35041

[9] A. Zenisek, Discrete forms of Friedrichs' inequalities in the finite element method. R.A.I.R.O. Anal. num. 15 (1981), 265-286. | Numdam | MR 631681 | Zbl 0475.65072

[10] A. Zenisek, Nonhomogeneous boundary conditions and curved triangular finite elements. Apl. Mat. (1981), 121-141. | MR 612669 | Zbl 0475.65073