The finite element solution of second order elliptic problems with the Newton boundary condition
Applications of Mathematics, Tome 28 (1983) no. 6, pp. 430-456
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The convergence of the finite element solution for the second order elliptic problem in the $n$-dimensional bounded domain $(n\geq 2)$ with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the $H^1$ and $L_2$ norms are obtained.
The convergence of the finite element solution for the second order elliptic problem in the $n$-dimensional bounded domain $(n\geq 2)$ with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the $H^1$ and $L_2$ norms are obtained.
DOI : 10.21136/AM.1983.104055
Classification : 35J25, 65N15, 65N30
Keywords: convergence; finite element; Newton boundary condition; simplicial isoparametric elements; error estimates
@article{10_21136_AM_1983_104055,
     author = {\v{C}erm\'ak, Libor},
     title = {The finite element solution of second order elliptic problems with the {Newton} boundary condition},
     journal = {Applications of Mathematics},
     pages = {430--456},
     year = {1983},
     volume = {28},
     number = {6},
     doi = {10.21136/AM.1983.104055},
     mrnumber = {0723203},
     zbl = {0542.65063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104055/}
}
TY  - JOUR
AU  - Čermák, Libor
TI  - The finite element solution of second order elliptic problems with the Newton boundary condition
JO  - Applications of Mathematics
PY  - 1983
SP  - 430
EP  - 456
VL  - 28
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104055/
DO  - 10.21136/AM.1983.104055
LA  - en
ID  - 10_21136_AM_1983_104055
ER  - 
%0 Journal Article
%A Čermák, Libor
%T The finite element solution of second order elliptic problems with the Newton boundary condition
%J Applications of Mathematics
%D 1983
%P 430-456
%V 28
%N 6
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104055/
%R 10.21136/AM.1983.104055
%G en
%F 10_21136_AM_1983_104055
Čermák, Libor. The finite element solution of second order elliptic problems with the Newton boundary condition. Applications of Mathematics, Tome 28 (1983) no. 6, pp. 430-456. doi: 10.21136/AM.1983.104055

[1] P. G. Ciarlet: The Finite Element Method for Elliptic Problems. North-Holland. Amsterdam. 1978. | MR | Zbl

[2] 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

[3] A. Kufner O. John S. Fučík: Function Spaces. Academia. Praha, 1977. | MR

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

[5] J. Nedoma: The finite element solution of parabolic equations. Apl. Mat., 23 (1977), 408-438. | MR

[6] J. Nedoma: The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements. R.A.I.R.O. Numer. Anal., 13 (1979), 257-289. | MR | Zbl

[7] K. Rektorys: Variační metody. SNTL. Praha. 1974. English translation: Variational Methods. Reidel Co.. Dordrecht-Boston. 1977. | MR | Zbl

[8] R. Scott: Interpolated boundary conditions in the finite element method. SIAM J. Numer. Anal., 12 (1975), 404-427. | DOI | MR | Zbl

[9] G. Strang: Approximation in the finite element method. Numer. Math., 19 (1972), 81-98. | DOI | MR | Zbl

[10] M. Zlámal: Curved elements in the finite element method I. SIAM J. Numer. Anal., 10 (1973), 229-240. | DOI | MR

[11] M. Zlámal: Curved elements in the finite element method II. SIAM J. Numer. Anal., 11 (1974), 347-369. | DOI | MR

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

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

Cité par Sources :