| Title:
|
Semiregular finite elements in solving some nonlinear problems (English) |
| Author:
|
Zlámalová, Jana |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
53-77 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, under the maximum angle condition, the finite element method is analyzed for nonlinear elliptic variational problem formulated in [4]. In [4] the analysis was done under the minimum angle condition. (English) |
| Keyword:
|
finite element method |
| Keyword:
|
nonlinear elliptic problems |
| Keyword:
|
semiregular elements |
| Keyword:
|
maximum angle condition |
| Keyword:
|
effect of numerical integration |
| Keyword:
|
approximation of the boundary |
| MSC:
|
35J65 |
| MSC:
|
65N12 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 1066.65133 |
| idMR:
|
MR1808429 |
| DOI:
|
10.1023/A:1013779621231 |
| . |
| Date available:
|
2009-09-22T18:05:48Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134457 |
| . |
| Reference:
|
[1] P. G. Ciarlet: The Finite Element Method for Elliptic Problems.North-Holland Publishing Company, Amsterdam, 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[2] M. Feistauer, K. Najzar: Finite element approximation of a problem with a nonlinear Newton boundary condition.Numer. Math. 78 (1998), 403–425. MR 1603350, 10.1007/s002110050318 |
| Reference:
|
[3] M. Feistauer, V. Sobotíková: Finite element approximation of nonlinear elliptic problems with discontinuous coefficients.RAIRO Modél. Math. Anal. Numér. 24 (1990), 457–500. MR 1070966, 10.1051/m2an/1990240404571 |
| Reference:
|
[4] M. Feistauer, A. Ženíšek: Finite element solution of nonlinear elliptic problems.Numer. Math. 50 (1987), 451–475. MR 0875168 |
| Reference:
|
[5] M. Křížek: On semiregular families of triangulations and linear interpolation.Appl. Math. 36 (1991), 223–232. MR 1109126 |
| Reference:
|
[6] A. Kufner, O. John and S. Fučík : Function Spaces.Academia, Praha, 1977. MR 0482102 |
| Reference:
|
[7] J. Nečas: Les Métodes Directes en Théorie des Equations Elliptiques.Academia-Masson, Prague-Paris, 1967. MR 0227584 |
| Reference:
|
[8] L. A. Oganesian, L. A Rukhovec: Variational-Difference Methods for the Solution of Elliptic Problems.Izd. Akad. Nauk ArSSR, Jerevan, 1979. (Russian) |
| Reference:
|
[9] A. Ženíšek: Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations.Academic Press, London, 1990. MR 1086876 |
| Reference:
|
[10] A. Ženíšek: The maximum angle condition in the finite element method for monotone problems with applications in magnetostatics.Numer. Math. 71 (1995), 399–417. MR 1347576, 10.1007/s002110050151 |
| Reference:
|
[11] A. Ženíšek: Finite element variational crimes in the case of semiregular elements.Appl. Math. 41 (1996), 367–398. MR 1404547 |
| Reference:
|
[12] A. Ženíšek: The use of semiregular finite elements.In: Proceedings of EQUADIFF, Conference on Differential Equations and Their Applications (R. P. Agarwal, F. Neuman and J. Vosmanský, eds.), Masaryk University, Brno & Electronic Publishing House, Stony Brook, New York, 1998, pp. 201–251. |
| Reference:
|
[13] M. Zlámal: Curved elements in the finite element method I .SIAM J. Numer. Anal. 10 (1973), 229–240. MR 0395263, 10.1137/0710022 |
| . |
