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Abstract:

An average interpolation is introduced for 3-rectangles and tetrahedra, and optimal order error estimates in the H1 norm are proved. The constant in the estimate depends "weakly" (improving the results given in Durán (Math. Comp. 68 (1999) 187-199) on the uniformity of the mesh in each direction. For tetrahedra, the constant also depends on the maximum angle of the element. On the other hand, merging several known results (Acosta and Durán, SIAM J. Numer. Anal. 37 (1999) 18-36; Durán, Math. Comp. 68 (1999) 187-199; Krizek, SIAM J. Numer. Anal. 29 (1992) 513-520; A1 Shenk, Math. Comp. 63 (1994) 105-119), we prove optimal order error for the P1-Lagrange interpolation in W1,p, > 2, with a constant depending on p as well as the maximum angle of the element. Again, under the maximum angle condition, optimal order error estimates are obtained in the H1 norm for higher degree interpolations. © 2001 Elsevier Science B.V. All rights reserved.

Registro:

Documento: Artículo
Título:Lagrange and average interpolation over 3D anisotropic elements
Autor:Acosta, G.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas-Pab. L, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Palabras clave:Anisotropic elements; Average interpolation; Lagrange interpolation; Maximum angle condition; Angle measurement; Anisotropy; Error analysis; Estimation; Lagrange interpolation; Interpolation; mathematical method
Año:2001
Volumen:135
Número:1
Página de inicio:91
Página de fin:109
DOI: http://dx.doi.org/10.1016/S0377-0427(00)00564-1
Título revista:Journal of Computational and Applied Mathematics
Título revista abreviado:J. Comput. Appl. Math.
ISSN:03770427
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03770427_v135_n1_p91_Acosta

Referencias:

  • Acosta, G., Durán, R.G., The maximum angle condition for mixed and nonconforming elements. Application to the Stokes equations (1999) SIAM J. Numer. Anal, 37, pp. 18-36
  • Acosta, G., Durán, R.G., Error estimates for 21 isoparametric elements satisfying a weak angle condition SIAM J. Numer. Anal, , in press
  • Apel, T., (1999) Anisotropic Finite Elements: Local Estimates and Applications, , preprint SFB393/99-03, Technische Univ. Chemnitz
  • Babuška, I., Aziz, A.K., On the angle condition in the finite element method (1976) SIAM J. Numer. Anal, 13, pp. 214-226
  • Brenner, S.C., Scott, L.R., (1994) The Mathematical Theory of Finite Element Methods, Texts in Applied Mathematics, 15. , Springer, Berlin
  • Ciarlet, P.G., (1978) The Finite Element Method for Elliptic Problems, , North-Holland, Amsterdam
  • Clement, P., Approximation by finite element functions using local regularizations (1975) Rev. Fran. Autom. Inform. Rech. Oper. Ser. Rouge Anal. Numer, 2 R, pp. 77-84
  • Durán, R.G., Error estimates for 3-d narrow finite elements (1999) Math. Comp, 68, pp. 187-199
  • Jamet, P., Estimations d'erreur pour des éléments finis droits presque dégénérés (1976) RAIRO Anal. Numér, 10, pp. 46-61
  • Krízek, M., On the maximum angle conditions for linear tetrahedral elements (1992) SIAM J. Numer. Anal, 29, pp. 513-520
  • Schultz, M.H., (1973) Spline Analysis, , Prentice-Hall, Englewood Cliffs, NJ
  • Al Shenk, N., Uniform error estimates for certain narrow Lagrange finite elements (1994) Math. Comp, 63, pp. 105-119
  • Scott, L.R., Zhang, S., Finite element interpolation of non-smooth functions satisfying boundary conditions (1990) Math. Comp, 54, pp. 483-493
  • Zenisek, A., Vanmaele, M., The interpolation theorem for narrow quadrilateral isoparametric finite elements (1995) Numer. Math, 72, pp. 123-141
  • Zenisek, A., Vanmaele, M., Applicability of the Bramble Hilbert lemma in interpolation problems of narrow quadrilateral isoparametric finite elements (1995) J. Comput. Appl. Math, 63, pp. 109-122

Citas:

---------- APA ----------
(2001) . Lagrange and average interpolation over 3D anisotropic elements. Journal of Computational and Applied Mathematics, 135(1), 91-109.
http://dx.doi.org/10.1016/S0377-0427(00)00564-1
---------- CHICAGO ----------
Acosta, G. "Lagrange and average interpolation over 3D anisotropic elements" . Journal of Computational and Applied Mathematics 135, no. 1 (2001) : 91-109.
http://dx.doi.org/10.1016/S0377-0427(00)00564-1
---------- MLA ----------
Acosta, G. "Lagrange and average interpolation over 3D anisotropic elements" . Journal of Computational and Applied Mathematics, vol. 135, no. 1, 2001, pp. 91-109.
http://dx.doi.org/10.1016/S0377-0427(00)00564-1
---------- VANCOUVER ----------
Acosta, G. Lagrange and average interpolation over 3D anisotropic elements. J. Comput. Appl. Math. 2001;135(1):91-109.
http://dx.doi.org/10.1016/S0377-0427(00)00564-1