Artículo
Durán, R.G. "Error estimates for 3-d narrow finite elements" (1999) Mathematics of Computation. 68(225):187-199
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Abstract:
We obtain error estimates for finite element approximations of the lowest degree valid uniformly for a class of three-dimensional narrow elements. First, for the Lagrange interpolation we prove optimal error estimates, both in order and regularity, in Lp for p > 2. For p = 2 it is known that this result is not true. Applying extrapolation results we obtain an optimal order error estimate for functions sligthly more regular than H2. These results are valid both for tetrahedral and rectangular elements. Second, for the case of rectangular elements, we obtain optimal, in order and regularity, error estimates for an average interpolation valid for functions in W1+s,p with 1 ≤ p ≤ ∞ and 0 ≤ s ≤ 1.
Registro:
| Documento: | Artículo |
| Título: | Error estimates for 3-d narrow finite elements |
| Autor: | Durán, R.G. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina |
| Año: | 1999 |
| Volumen: | 68 |
| Número: | 225 |
| Página de inicio: | 187 |
| Página de fin: | 199 |
| Título revista: | Mathematics of Computation |
| Título revista abreviado: | Math. Comput. |
| ISSN: | 00255718 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n225_p187_Duran |
Referencias:
- Babuska, I., Aziz, A.K., On the angle condition in the finite element, method (1976) SIAM J. Numer. Anal., 13, pp. 214-226
- MR, 56, p. 13700
- Barnhill, R.E., Gregory, J.A., Interpolation remainder theory from Taylor expansions on triangles (1976) Numer. Math., 25, pp. 401-408
- MR, 56, p. 7253
- Brenner, S.C., Scott, L.R., The mathematical theory of finite element methods (1994) Texts in Applied Mathematics, 15. , Springer-Verlag
- MR, 95 F, p. 65001
- Ciarlet, P.G., (1978) The Finite Element Method for Elliptic Problems, , North Holland
- MR, 58, p. 25001
- Clement, P., Approximation by finite element functions using local regularization (1975) RAIRO Anal. Numér., 9, pp. 77-84
- MR, 53, p. 4569
- Dechevski, L.T., Quak, E., On the Bramble-Hubert lemma (1990) Numer. Funct. Anal. and Optimiz., 11, pp. 485-495
- MR, 91 K, p. 46027
- Dupont, T., Scott, R., Constructive polynomial approximation in Sobolev spaces (1980) Recent Advances in Numerical Analysis, , (C.de Boor and G. Golub, eds.), Academic Press
- MR, 80 J, p. 41055
- Polynomial approximation of functions in Sobolev spaces (1980) Math. Comp., 34, pp. 441-463
- MR, 81 H, p. 65014
- Durán, R.G., On polynomial approximation in Sobolev spaces (1983) SIAM J. Numer. Anal., 20, pp. 985-988
- MR, 85 E, p. 42010
- Gregory, J.A., Error bounds for linear interpolation on triangles (1976) The Mathematics of Finite Elements and Applications II, pp. 163-170. , Academic Press
- MR, 56, p. 16995
- Grisvard, P., (1985) Elliptic Problems in Nonsmooth Domains, , Pitman
- MR, 86 M, p. 35044
- Hudson, S.M., Polynomial approximation in Sobolev spaces (1990) Indiana University Math. J., 39, pp. 199-228
- MR, 91 H, p. 41007
- Jamet, P., Estimations d'erreur pour des elements finis droits presque dégénérés (1976) RAIRO Anal. Numér, 10, pp. 46-61
- MR, 56, p. 13521
- Jawerth, B., Milman, M., Extrapolation theory with applications (1991) Memoirs Amer. Math. Soc., 440
- MR, 91 I, p. 46092
- Krízek, M., On semiregular families of triangulations and linear interpolation (1991) Applications of Math., 36, pp. 223-232
- MR, 92 E, p. 65010
- On the maximum angle condition for linear tetrahedral elements (1992) SIAM J. Numer. Anal., 29, pp. 513-520
- MR, 92 K, p. 65165
- Ladyzhenskaya, Solonnikov, Uraltceva, Linear and quasilinear parabolic differential equations (1968) Transl. of Math. Mon., 23. , AMS
- Milman, M., Extrapolation and optimal decompositions (1994) Lecture Notes in Mathematics, 1580. , Springer-Verlag, Berlin
- MR, 96 A, p. 46133
- Personal communication; Schultz, M.H., (1973) Spline Analysis, , Prentice Hall
- MR, 50, p. 15270
- Scott, L.R., Zhang, S., Finite element interpolation of non-smooth functions satisfying boundary conditions (1990) Math. Comp., 54, pp. 483-493
- MR, 90 J, p. 65021
- Al Shenk, N., Uniform error estimates for certain narrow Lagrange finite elements (1994) Math. Comp., 63, pp. 105-119
- MR, 94 I, p. 65119
- Stein, E., (1970) Singular Integrals and Differentiability Properties of Functions, , Princeton University Press
- MR, 44, p. 7280
- Zenísek, A., Vanmaele, M., The interpolation theorem for narrow quadrilateral isoparametric finite elements (1995) Numer. Math., 72, pp. 123-141
- MR, 97 I, p. 65157
Citas:
---------- APA ----------
(1999) . Error estimates for 3-d narrow finite elements. Mathematics of Computation, 68(225), 187-199.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n225_p187_Duran [ ]
---------- CHICAGO ----------
Durán, R.G. "Error estimates for 3-d narrow finite elements" . Mathematics of Computation 68, no. 225 (1999) : 187-199.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n225_p187_Duran [ ]
---------- MLA ----------
Durán, R.G. "Error estimates for 3-d narrow finite elements" . Mathematics of Computation, vol. 68, no. 225, 1999, pp. 187-199.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n225_p187_Duran [ ]
---------- VANCOUVER ----------
Durán, R.G. Error estimates for 3-d narrow finite elements. Math. Comput. 1999;68(225):187-199.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v68_n225_p187_Duran [ ]
