| Title:
|
On semiregular families of triangulations and linear interpolation (English) |
| Author:
|
Křížek, Michal |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
1991 |
| Pages:
|
223-232 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider triangulations formed by triangular elements. For the standard linear interpolation operator $\pi__h$ we prove the interpolation order to be $\left\|v-{\pi__h} v\right\|_{1,p}\leq Ch\left|v\right|_{2,p}$ for $p>1$ provided the corresponding family of triangulations is only semiregular. In such a case the well-known Zlámal's condition upon the minimum angle need not be satisfied. (English) |
| Keyword:
|
finite elements |
| Keyword:
|
linear interpolation |
| Keyword:
|
maximum angle condition |
| Keyword:
|
Zlámal’s condition |
| MSC:
|
41A05 |
| MSC:
|
65D05 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0728.41003 |
| idMR:
|
MR1109126 |
| DOI:
|
10.21136/AM.1991.104461 |
| . |
| Date available:
|
2008-05-20T18:41:44Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104461 |
| . |
| Reference:
|
[1] I. Babuška A. K. Aziz: On the angle condition in the finite element method.SIAM J. Numer. Anal. 13 (1976), 214-226. MR 0455462, 10.1137/0713021 |
| Reference:
|
[2] R. E. Barnhill J. A. Gregory: Sard kernel theorems on triangular domains with application to finite element error bounds.Numer. Math. 25 (1976), 215-229. MR 0458000 |
| Reference:
|
[3] P. G. Ciarlet: The finite element method for elliptic problems.North-Holland, Amsterdam, New York, Oxford, 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[4] J. A. Gregory: Error bounds for linear interpolation on triangles.(in Proc. MAFELAP II, ed. J. R. Whiteman). Academic Press, London, 1976, 163-170. MR 0458795 |
| Reference:
|
[5] P. Jamet: Estimations d'erreur pour des éléments finis droits presque dégénérés.RAIRO Anal. Numér. 10 (1976), 43-60. MR 0455282 |
| Reference:
|
[6] P. Jamet: Estimations de l'erreur d'interpolation dans un domaine variable et applications aux éléments finis quadrilatéraux dégénérés.Méthodes Numériques en Mathématiques Appliquées, Presses de l'Université de Montreal, 55-100. MR 0445863 |
| Reference:
|
[7] M. Křížek: On semiregular families of decompositions of a polyhedron into tetrahedra and linear interpolation.(in Proc. of the 6th Conf. Mathematical Methods in Engineering). ŠKODA, Plzeň, 1991, 269-274. |
| Reference:
|
[8] M. Křížek P. Neittaanmäki: Finite element approximation of variational problems and applications.Pitman Monographs and Surveys in Pure and Applied Mathematics vol. 50, Longman Scientific & Technical, Harlow, 1990. MR 1066462 |
| Reference:
|
[9] J. Nečas: Les rnéthodes directes en théorie des équations elliptiques.Academia, Prague, 1967. MR 0227584 |
| Reference:
|
[10] G. Strang G. J. Fix: An analysis of the finite element method.Prentice-Hall, INC., New Jersey, London, 1973. MR 0443377 |
| Reference:
|
[11] J. L. Synge: The hypercircle in mathematical physics.Cambridge University Press, Cambridge, 1957. Zbl 0079.13802, MR 0097605 |
| Reference:
|
[12] A. Ženíšek: The convergence of the finite element method for boundary value problems of a system of elliptic equations.Apl. Mat. 14 (1969), 355- 377. MR 0245978 |
| Reference:
|
[13] M. Zlámal: On the finite element method.Numer. Math. 12 (1968), 394-409. MR 0243753, 10.1007/BF02161362 |
| . |
