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Optimal design formulations for finite element grid adaptation

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Sensitivity of Functionals with Applications to Engineering Sciences

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1086))

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References

  1. Babuśka, I., J. Chandra and J. E. Flaherty (eds), Proc. Symp. on Adaptive Comp. Methods for Partial Differential Equations, SIAM, Philadelphia, 1983.

    Google Scholar 

  2. Ghia, K. and Ghia, U., Advances in Grid Generation, FED-Vol. 5, American Society of Mechanical Engineers, New York, 1983.

    MATH  Google Scholar 

  3. Oliveira, E.R. de A., "Optimization of finite element solution," Proc. 3rd Conf. Matrix Methods in Structural Mechanics, Wright-Patterson Air Force Base, Ohio, 1971.

    Google Scholar 

  4. Prager, William, "A note on the optimal choice of finite element grids," Comp. Meths. Appld. Mech. & Engrg., 6, 363–366, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  5. Tang, J. W. and Turcke, "Characteristics of optimal grids," Compt. Method. Appl. Mech. Eng., 11, 31–37, 1977.

    Article  Google Scholar 

  6. Masur, E. F., "Some remarks on the optimal choice of finite element grids," Comp. Meths. Appl. Mechs. & Engrg., 14, 237–248, 1978.

    Article  MATH  Google Scholar 

  7. Melosh, R. J., and Marcal, P. V., "An energy basis for mesh refinement of structural continua," Int. J. Num. Meth. Engrg., 11, 1083–1091, 1977.

    Article  MATH  Google Scholar 

  8. Turcke, D. J. and McNeice, G. M., "Guidelines for selecting finite element grids based on an optimization study," Computers & Structures, 4, 499–519, 1974.

    Article  Google Scholar 

  9. Shephard, M. S., Gallagher, R. H. and Abel, J. F., "The synthesis of nearoptimum finite element meshes with iterative computer graphics," Int. J. Num. Meth. Engrg., 15, 1021–1039, 1980.

    Article  MATH  Google Scholar 

  10. Babuska, I. and Rheinboldt, W. C., "Reliable error estimation and mesh adaptation for the finite element method," in J. T. Oden, Ed., Computational Methods in Nonlinear Mechanics, North-Holland, Amsterdam, 67–108, 1980.

    Google Scholar 

  11. Babuska, I. and Rheinboldt, W. C., "Error estimates for adaptive finite element computations," SIAM J. Num. Anal., 15, 736–754, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  12. Babuska, I. and Rheinboldt, W. C., "Computer error estimates and adaptive processes for some nonlinear structural problems," Comp. Meth. Applied Mech. Engrg., 34, 895–937, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  13. Babuska, I. and Szabo, B., "On the rates of convergence of the finite element methods," Int. J. Num. Meth. Engrg., 18, 323–341, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  14. Sewell, G., "An adaptive computer program for the solution of DIV(P(x,y)GRAD U)=F(x,y,U) on a polygonal region," in J. R. Whiteman, Ed., The Mathematics of Finite Elements and Applications, II, MAFGLAP, 1975; Academic Press, London, 1976.

    Google Scholar 

  15. Zienkiewicz, O. C., S. R. Gago, J. P. de Gago, and Kelly, D. W., "The hierarchical concept in finite element analysis," Computers & Structures, 16, 53–65, 1983.

    Article  MATH  Google Scholar 

  16. Felippa, C. A., "Optimization of finite element grids by direct energy search," Appl. Math. Modelling, 1, 93–96, 1976.

    Article  MATH  Google Scholar 

  17. Felippa, C. A., "Numerical experiments in finite element grid optimization by direct energy search," Appl. Math. Modelling, 1, 239–244, 1977.

    Article  Google Scholar 

  18. Shephard, M. S., "Finite element grid optimization," ASME Special Publication PVP-38, AISME, New York, 1979.

    Google Scholar 

  19. Rossow, M. P. and Katz, I. N., "Hierarchical finite elements and precomputed arrays," Int. J. Num. Meth. Engrg., 12, 977–999, 1978.

    Article  MATH  Google Scholar 

  20. Díaz Bermúdez, Alejandro R., "Optimization of finite element grids using interpolation error," Ph.D. Thesis in Aerospace Engineering, The University of Michigan, Ann Arbor, 1982.

    Google Scholar 

  21. Necas, J. and Hlavacek, L., Mathematical Theory of Elastic and Elastic-Plastic Bodies, Elsevier, Amsterdam, 1981.

    MATH  Google Scholar 

  22. Ciarlet, P. G., Numerical Analysis of the Finite Element Methods, Les Presses de L'Université de Montréal, 1976.

    Google Scholar 

  23. Nakazawa, S., and O. Zienkiewicz, (private communication).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Intevep/Ingenieria General, Apartado 76343, 1080A, Caracas, Venezuela

    Alejandro R. Diaz

  2. College of Engineering, The University of Michigan, 48109-2140, Ann Arbor, MI, U.S.A.

    Noboru Kikuchi & J. E. Taylor

Authors
  1. Alejandro R. Diaz
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  2. Noboru Kikuchi
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  3. J. E. Taylor
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Editor information

Vadim Komkov

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© 1984 Springer-Verlag

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Diaz, A.R., Kikuchi, N., Taylor, J.E. (1984). Optimal design formulations for finite element grid adaptation. In: Komkov, V. (eds) Sensitivity of Functionals with Applications to Engineering Sciences. Lecture Notes in Mathematics, vol 1086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073069

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  • DOI: https://doi.org/10.1007/BFb0073069

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13871-6

  • Online ISBN: 978-3-540-39061-9

  • eBook Packages: Springer Book Archive

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