| Title:
|
The finite element solution of second order elliptic problems with the Newton boundary condition (English) |
| Author:
|
Čermák, Libor |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
6 |
| Year:
|
1983 |
| Pages:
|
430-456 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
convergence |
| Keyword:
|
finite element |
| Keyword:
|
Newton boundary condition |
| Keyword:
|
simplicial isoparametric elements |
| Keyword:
|
error estimates |
| MSC:
|
35J25 |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0542.65063 |
| idMR:
|
MR0723203 |
| DOI:
|
10.21136/AM.1983.104055 |
| . |
| Date available:
|
2008-05-20T18:23:30Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104055 |
| . |
| Reference:
|
[1] P. G. Ciarlet: The Finite Element Method for Elliptic Problems.North-Holland. Amsterdam. 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[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 0421108 |
| Reference:
|
[3] A. Kufner O. John S. Fučík: Function Spaces.Academia. Praha, 1977. MR 0482102 |
| Reference:
|
[4] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia. Prague. 1967. MR 0227584 |
| Reference:
|
[5] J. Nedoma: The finite element solution of parabolic equations.Apl. Mat., 23 (1977), 408-438. MR 0508545 |
| Reference:
|
[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. Zbl 0413.65080, MR 0543935 |
| Reference:
|
[7] K. Rektorys: Variační metody.SNTL. Praha. 1974. English translation: Variational Methods. Reidel Co.. Dordrecht-Boston. 1977. Zbl 0371.35001, MR 0487653 |
| Reference:
|
[8] R. Scott: Interpolated boundary conditions in the finite element method.SIAM J. Numer. Anal., 12 (1975), 404-427. Zbl 0357.65082, MR 0386304, 10.1137/0712032 |
| Reference:
|
[9] G. Strang: Approximation in the finite element method.Numer. Math., 19 (1972), 81-98. Zbl 0221.65174, MR 0305547, 10.1007/BF01395933 |
| Reference:
|
[10] M. Zlámal: Curved elements in the finite element method I.SIAM J. Numer. Anal., 10 (1973), 229-240. MR 0395263, 10.1137/0710022 |
| Reference:
|
[11] M. Zlámal: Curved elements in the finite element method II.SIAM J. Numer. Anal., 11 (1974), 347-369. MR 0343660, 10.1137/0711031 |
| Reference:
|
[12] A. Ženíšek: Nonhomogeneous boundary conditions and curved triangular finite elements.Apl. Mat., 26 (1981), 121-141. MR 0612669 |
| Reference:
|
[13] A. Ženíšek: Discrete forms of Friedrichs' inequalities in the finite element method.R.A.I.R.O. Numer. Anal., 15 (1981), 265-286. Zbl 0475.65072, MR 0631681 |
| . |
