A note on a discrete form of Friedrichs' inequality

Libor Čermák

Aplikace matematiky (1983)

  • Volume: 28, Issue: 6, page 457-466
  • ISSN: 0862-7940

Abstract

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The proof of the Friedrichs' inequality on the class of finite dimensional spaces used in the finite element method is given. In particular, the approximate spaces generated by simplicial isoparametric elements are considered.

How to cite

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Čermák, Libor. "A note on a discrete form of Friedrichs' inequality." Aplikace matematiky 28.6 (1983): 457-466. <http://eudml.org/doc/15323>.

@article{Čermák1983,
abstract = {The proof of the Friedrichs' inequality on the class of finite dimensional spaces used in the finite element method is given. In particular, the approximate spaces generated by simplicial isoparametric elements are considered.},
author = {Čermák, Libor},
journal = {Aplikace matematiky},
keywords = {finite element method; simplicial isoparametric elements; Friedrichs’ inequality; finite element method; simplicial isoparametric elements; Friedrichs' inequality},
language = {eng},
number = {6},
pages = {457-466},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on a discrete form of Friedrichs' inequality},
url = {http://eudml.org/doc/15323},
volume = {28},
year = {1983},
}

TY - JOUR
AU - Čermák, Libor
TI - A note on a discrete form of Friedrichs' inequality
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 6
SP - 457
EP - 466
AB - The proof of the Friedrichs' inequality on the class of finite dimensional spaces used in the finite element method is given. In particular, the approximate spaces generated by simplicial isoparametric elements are considered.
LA - eng
KW - finite element method; simplicial isoparametric elements; Friedrichs’ inequality; finite element method; simplicial isoparametric elements; Friedrichs' inequality
UR - http://eudml.org/doc/15323
ER -

References

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  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 and London. 1972. (1972) MR0421108
  2. L. Čermák, The finite element solution of second order elliptic problems with the Newton boundary condition, Apl. Mat., 28 (1983), 430-456. (1983) MR0723203
  3. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia. Prague. 1967. (1967) MR0227584
  4. K. Yosida, Functional Analysis, Springer-Verlag. Berlin-Heidelberg-New York. 1966. (1966) 
  5. A. Ženíšek, Nonhomogeneous boundary conditions and curved triangular finite elements, Apl. Mat., 26 (1981), 121-141. (1981) MR0612669
  6. A. Ženíšek, Discrete forms of Friedrichs' inequalities in the finite element method, R.A.LR.O Numer. Anal., 15 (1981), 265-286. (1981) Zbl0475.65072MR0631681

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