Estimadores de error y optimización de mallas en el método de elementos finitos
DOI:
https://doi.org/10.22199/S07160917.1985.0009.00002Keywords:
operadores lineales, optimización de mallas, logaritmosAbstract
Se considera el problema de contorno vinculado al operador lineal autoadjunto de segundo orden, y se deducen detalladamente los estimadores de error asociados a la solución de elementos finitos. Esto permite, mediante técnicas clásicas de interpolación, el diseño de nuevos logaritmos de optimización de mallas, los que en base a un análisis local sitúan casi-óptimamente un número fijo de nodos en un dominio unidimensional.References
[1] BABUSKA, I.; MILLER, A.: "A-posteriori error estimates and adaptive techniques for the finite element method". University of Maryland, Institute for Physical Science and Technology, Technical Note BN-968, June 1981.
[2] BABUSKA, I.; MILLER, A.; VOGELIUS, M.: "Adaptive methods and error estimation for elliptic problems of structural mechanics". University of Maryland, Inst. for Phys. Science and Techn., Technical Note BN-1009, June 1983.
[3] BABUSKA, I.; RHEINBOLDT, W.: "Error estimates for adaptat1ve finite element computation". SIAM Journ. Num. Anal., Vol. 15, N° 4, 1978, pp. 736-754.
[4] BABUSKA, I.; RHEINBOLDT, W.: "A-posteriori error estimates for the finite element method". Int. Jour. for Numer. Methods in Engineerinq, 12, 1597-1615, (1978).
[5] BABUSKA, I,; RHEINBOLDT, W.: "Analysis of optimal finite element meshes in :?1 " Math. of Comput. 33, pp. 435-463, 1979.
[6] BABUSKA, I,; VOGELIUS, M.: "Feedback and adaptive finite element solution of one dimensional boundary value problems". University of Maryland, Inst. for Phys. Se. and Tech., Technical Note BN-1006, June 1983. Numer. Mathem, 44, pp. 75-102, 1984.
[7] BABUSKA, I.; GAGO, S.; KELLY, D.; ZIENKIEWICZ, O.: "A-posteriori error analysis and adaptive process in the finite element method: Part I -Error Analysis".Inter. Journ. Numer. Methods in Engineering, Vol 19, pp. 1593-1619, 1983.
[8] BULIRSCH, R.; STOER, J.: "Introduction to Numerical Analysis". Springer Verlag, New York, 1980.
[9] GATICA, G.: "A new feedback finite element method and alternative algorithms for grid optimization", In preparation.
[10] RHEINBOLDT, W: "Adaptive mesh refinementd process for finite element solutions". Inter. Journal for Numer. Methods in Engineering, 17, pp. 649-6621 1981.
[2] BABUSKA, I.; MILLER, A.; VOGELIUS, M.: "Adaptive methods and error estimation for elliptic problems of structural mechanics". University of Maryland, Inst. for Phys. Science and Techn., Technical Note BN-1009, June 1983.
[3] BABUSKA, I.; RHEINBOLDT, W.: "Error estimates for adaptat1ve finite element computation". SIAM Journ. Num. Anal., Vol. 15, N° 4, 1978, pp. 736-754.
[4] BABUSKA, I.; RHEINBOLDT, W.: "A-posteriori error estimates for the finite element method". Int. Jour. for Numer. Methods in Engineerinq, 12, 1597-1615, (1978).
[5] BABUSKA, I,; RHEINBOLDT, W.: "Analysis of optimal finite element meshes in :?1 " Math. of Comput. 33, pp. 435-463, 1979.
[6] BABUSKA, I,; VOGELIUS, M.: "Feedback and adaptive finite element solution of one dimensional boundary value problems". University of Maryland, Inst. for Phys. Se. and Tech., Technical Note BN-1006, June 1983. Numer. Mathem, 44, pp. 75-102, 1984.
[7] BABUSKA, I.; GAGO, S.; KELLY, D.; ZIENKIEWICZ, O.: "A-posteriori error analysis and adaptive process in the finite element method: Part I -Error Analysis".Inter. Journ. Numer. Methods in Engineering, Vol 19, pp. 1593-1619, 1983.
[8] BULIRSCH, R.; STOER, J.: "Introduction to Numerical Analysis". Springer Verlag, New York, 1980.
[9] GATICA, G.: "A new feedback finite element method and alternative algorithms for grid optimization", In preparation.
[10] RHEINBOLDT, W: "Adaptive mesh refinementd process for finite element solutions". Inter. Journal for Numer. Methods in Engineering, 17, pp. 649-6621 1981.
Published
2018-03-27
How to Cite
[1]
G. N. Gatica Pérez, “Estimadores de error y optimización de mallas en el método de elementos finitos”, Proyecciones (Antofagasta, On line), vol. 4, no. 9, pp. 11-58, Mar. 2018.
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