Geodesic
A note on a discrete form of Friedrichs' inequality
Applications of Mathematics, Tome 28 (1983) no. 6, pp. 457-466
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1983.104056
Classification : 35J25, 65N30
Keywords: finite element method; simplicial isoparametric elements; Friedrichs’ inequality 
@article{10_21136_AM_1983_104056,
     author = {\v{C}erm\'ak, Libor},
     title = {A note on a discrete form of {Friedrichs'} inequality},
     journal = {Applications of Mathematics},
     pages = {457--466},
     year = {1983},
     volume = {28},
     number = {6},
     doi = {10.21136/AM.1983.104056},
     mrnumber = {0723204},
     zbl = {0537.65073},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104056/}
}
TY  - JOUR
AU  - Čermák, Libor
TI  - A note on a discrete form of Friedrichs' inequality
JO  - Applications of Mathematics
PY  - 1983
SP  - 457
EP  - 466
VL  - 28
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104056/
DO  - 10.21136/AM.1983.104056
LA  - en
ID  - 10_21136_AM_1983_104056
ER  - 
%0 Journal Article
%A Čermák, Libor
%T A note on a discrete form of Friedrichs' inequality
%J Applications of Mathematics
%D 1983
%P 457-466
%V 28
%N 6
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104056/
%R 10.21136/AM.1983.104056
%G en
%F 10_21136_AM_1983_104056
Čermák, Libor. A note on a discrete form of Friedrichs' inequality. Applications of Mathematics, Tome 28 (1983) no. 6, pp. 457-466. doi: 10.21136/AM.1983.104056

[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. | MR

[2] L. Čermák: The finite element solution of second order elliptic problems with the Newton boundary condition. Apl. Mat., 28 (1983), 430-456. | MR

[3] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia. Prague. 1967. | MR

[4] K. Yosida: Functional Analysis. Springer-Verlag. Berlin-Heidelberg-New York. 1966.

[5] A. Ženíšek: Nonhomogeneous boundary conditions and curved triangular finite elements. Apl. Mat., 26 (1981), 121-141. | MR

[6] A. Ženíšek: Discrete forms of Friedrichs' inequalities in the finite element method. R.A.LR.O Numer. Anal., 15 (1981), 265-286. | MR | Zbl

Cité par Sources :