On semiregular families of triangulations and linear interpolation
Křížek, Michal
Applications of Mathematics, Tome 36 (1991), p. 223-232 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1991-01-01
Classification:  41A05,  65D05,  65N30 
@article{104461,
     author = {Michal K\v r\'\i \v zek},
     title = {On semiregular families of triangulations and linear interpolation},
     journal = {Applications of Mathematics},
     volume = {36},
     year = {1991},
     pages = {223-232},
     zbl = {0728.41003},
     mrnumber = {1109126},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104461}
}

Křížek, Michal. On semiregular families of triangulations and linear interpolation. Applications of Mathematics, Tome 36 (1991) pp. 223-232. http://gdmltest.u-ga.fr/item/104461/

I. Babuška A. K. Aziz On the angle condition in the finite element method, SIAM J. Numer. Anal. 13 (1976), 214-226. (1976) | Article | MR 0455462

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. (1976) | MR 0458000

P. G. Ciarlet The finite element method for elliptic problems, North-Holland, Amsterdam, New York, Oxford, 1978. (1978) | MR 0520174 | Zbl 0383.65058

J. A. Gregory Error bounds for linear interpolation on triangles, (in Proc. MAFELAP II, ed. J. R. Whiteman). Academic Press, London, 1976, 163-170. (1976) | MR 0458795

P. Jamet Estimations d'erreur pour des éléments finis droits presque dégénérés, RAIRO Anal. Numér. 10 (1976), 43-60. (1976) | MR 0455282

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

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. (1991)

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. (1990) | MR 1066462

J. Nečas Les rnéthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) | MR 0227584

G. Strang G. J. Fix An analysis of the finite element method, Prentice-Hall, INC., New Jersey, London, 1973. (1973) | MR 0443377

J. L. Synge The hypercircle in mathematical physics, Cambridge University Press, Cambridge, 1957. (1957) | MR 0097605 | Zbl 0079.13802

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. (1969) | MR 0245978

M. Zlámal On the finite element method, Numer. Math. 12 (1968), 394-409. (1968) | Article | MR 0243753