| Title:
|
Dual variational principles for an elliptic partial differential equation (English) |
| Author:
|
Vacek, Jiří |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
21 |
| Issue:
|
1 |
| Year:
|
1976 |
| Pages:
|
5-27 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Dual variational principles for an elliptic partial differential equation of the second order with combined boundary conditions are formulated. A posteriori error estimates are obtained and for some class of problems the convergence of approximate solutions of the dual problem is proved. A numerical example is presented.
The analysis of the approximate solutions suggests that especially when we are interested mainly in the values of co-normal derivatives on the boundary the dual method can serve an effective method for a approximate solution. () |
| MSC:
|
35B45 |
| MSC:
|
35J20 |
| MSC:
|
65M99 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0345.35035 |
| idMR:
|
MR0412594 |
| DOI:
|
10.21136/AM.1976.103619 |
| . |
| Date available:
|
2008-05-20T18:03:14Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103619 |
| . |
| Reference:
|
[1] Aubin J. P., Burchard H. G.: Some aspects of the method of the hypercircle applied to elliptic variational problems.1 - 68, Numerical solution of partial differential equations - II, SYNSPADE 1970, ed. B. Hubbard, Academic Press, New York 1971. MR 0285136 |
| Reference:
|
[2] Babuška I., Kellog R. D.: Numerical solution of the neutron diffusion equation in the presence of corners and interfaces.Numerical reactor calculations, Panel IAEA-SM-154/59, Vienna 1973. |
| Reference:
|
[3] Bramble J. H., Zlámal M.: Triangular elements in the finite element method.Math, of Соmр., 24, (1970), 809-821. MR 0282540 |
| Reference:
|
[4] Grenacher F.: A posteriori error estimates for elliptic partial differential equations.Technical Note BN-743, Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, 1972. |
| Reference:
|
[5] Kang C. M., Hansen K. F.: Finite element method for the neutron diffusion equation.Trans. Am. Nucl. Soc. 14 (1971), 199. |
| Reference:
|
[6] Kaper H. G., Leaf G. K., Lindeman A. J.: Applications of finite element method in reactor mathematics.ANL-7925, Argonne National Laboratory, Argonne, Illinois, 1972. |
| Reference:
|
[7] Nečas J.: Les méthodes directes en théorie des équations elliptiques.Academia, Praha 1967. MR 0227584 |
| Reference:
|
[8] Semenza L. A., Lewis E. E., Rossow E. C.: A finite element treatment of neutron diffusion.Trans. Am. Nucl. Soc. 14, (1971), 200. |
| Reference:
|
[9] Semenza L. A., Lewis E. E., Rossow E. C.: Dual finite element methods for neutron diffusion.Trans. Am. Nucl. Soc., 14 (1971), 662. |
| Reference:
|
[10] Strang G., Fix G. J.: An analysis of the finite element method.Prentice-Hall, Englewood Cliffs, New Jersey, 1973. Zbl 0356.65096, MR 0443377 |
| Reference:
|
[11] Taylor A. E.: Introduction to functional analysis.John Willey & Sons, New York, 1967. MR 0098966 |
| Reference:
|
[12] Vacek J.: Dual variational principles for neutron diffusion equation.thesis, MFF UK, Praha, 1974 (in Czech). |
| Reference:
|
[13] Yasinsky J. B., Kaplan S.: On the use of dual variational principles for the estimation of error in approximate solutions of diffusion problems.Nucl. Sci. Eng., 31 (1968), 80. 10.13182/NSE68-A18010 |
| Reference:
|
[14] Zlámal M., Ženíšek A.: Mathematical aspects of the finite element method.Trans. of ČSAV, 81 (1971), Praha. |
| . |
