On FE-grid relocation in solving unilateral boundary value problems by FEM

Jaroslav Haslinger; Pekka Neittaanmäki; Kimmo Salmenjoki

Applications of Mathematics (1992)

  • Volume: 37, Issue: 2, page 105-122
  • ISSN: 0862-7940

Abstract

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We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions. Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the plane elasticity problem with unilateral boundary conditions are given. In plane elasticity we consider problems with and without friction.

How to cite

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Haslinger, Jaroslav, Neittaanmäki, Pekka, and Salmenjoki, Kimmo. "On FE-grid relocation in solving unilateral boundary value problems by FEM." Applications of Mathematics 37.2 (1992): 105-122. <http://eudml.org/doc/15703>.

@article{Haslinger1992,
abstract = {We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions. Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the plane elasticity problem with unilateral boundary conditions are given. In plane elasticity we consider problems with and without friction.},
author = {Haslinger, Jaroslav, Neittaanmäki, Pekka, Salmenjoki, Kimmo},
journal = {Applications of Mathematics},
keywords = {unilateral boundary value problem; grid relocation; finite element methods; Poisson equation; numerical examples; nonlinear optimization; sequential quadratic programming code; FE-grid relocation; unilateral boundary value problem; grid relocation; finite element methods; Poisson equation; Numerical examples; nonlinear optimization; sequential quadratic programming code},
language = {eng},
number = {2},
pages = {105-122},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On FE-grid relocation in solving unilateral boundary value problems by FEM},
url = {http://eudml.org/doc/15703},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Haslinger, Jaroslav
AU - Neittaanmäki, Pekka
AU - Salmenjoki, Kimmo
TI - On FE-grid relocation in solving unilateral boundary value problems by FEM
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 2
SP - 105
EP - 122
AB - We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions. Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the plane elasticity problem with unilateral boundary conditions are given. In plane elasticity we consider problems with and without friction.
LA - eng
KW - unilateral boundary value problem; grid relocation; finite element methods; Poisson equation; numerical examples; nonlinear optimization; sequential quadratic programming code; FE-grid relocation; unilateral boundary value problem; grid relocation; finite element methods; Poisson equation; Numerical examples; nonlinear optimization; sequential quadratic programming code
UR - http://eudml.org/doc/15703
ER -

References

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  1. Babuška I., Rank E., An expert-system-like feedback approach in the fop-version of the finite element method, Finite Elements in Analysis and Design 3 (1987), 127-149. (1987) 
  2. Babuška I., Zienkiewicz O.C., Gago J., de A. Oliveira E.R. (eds.), Accuracy Estimates and Adaptive Refinements in Finite Element Computations, J. Wiley & Sons, Chichester, 1986. (1986) MR0879442
  3. Blum H., Lin Q., Rannacher R., 10.1007/BF01389427, Numerische Mathematik 49 (1986), 11-37. (1986) Zbl0594.65082MR0847015DOI10.1007/BF01389427
  4. Ciarlet P.G., The Finite Element Method for elliptic problems, North-Holland, Amsterdam, 1978. (1978) Zbl0383.65058MR0520174
  5. Delfour M., Payre G., Zolésio J. P., 10.1016/0045-7825(85)90095-7, Computational Methods in Applied Mechanics and Engineering 50 (1985), 231-261. (1985) MR0800331DOI10.1016/0045-7825(85)90095-7
  6. Guo B., Babuška I., 10.1007/BF00272624, Computational Mechanics, Part 2 1 (1986), 203-220. (1986) DOI10.1007/BF00272624
  7. Eriksson K., Johnson C., 10.1090/S0025-5718-1988-0929542-X, Mathematics of Computation 50 (1988), 361-383. (1988) Zbl0644.65080MR0929542DOI10.1090/S0025-5718-1988-0929542-X
  8. Haslinger J., Neittaanmäki P., Finite Element Approximation of Optimal Shape Design. Theory and Approximation, John Wiley & Sons, London, 1988. (1988) MR0982710
  9. Haslinger J., Neittaanmäki P., Salmenjoki K., On optimal mesh design for FEM in unilateral boundary value problems, MAFELAP VI, (J.R. Whiteman ed.) (1988), 103-114, Academic Press, London. (1988) MR0956891
  10. Hlaváček I., Haslinger J., Nečas J., Lovíšek J., Numerical Solution of Variational Inequalities, Springer Series in Applied Mathematical Sciences 66, Springer-Verlag, Berlin, 1988. (1988) 
  11. Jarusch H., 10.1137/0907075, SIAM Journal of Scientific and Statical Computations 4 (1986), 1105-1120. (1986) MR0857785DOI10.1137/0907075
  12. Kikuchi N., Finite Element Methods in Mechanics, Cambridge University Press, London, 1986. (1986) Zbl0587.73102
  13. Kikuchi N., Oden J. T., Contact Problems in Elasticity, SIAM Studies in Applied Mathematics, Philadelphia, 1988. (1988) Zbl0685.73002MR0961258
  14. Křížek M., Neittaanmäki P., 10.1007/BF00047538, Acta Applic. Math. 9 (1987), 175-198. (1987) MR0900263DOI10.1007/BF00047538
  15. Pironneau O., Optimal shape design for elliptic systems, Springer-Verlag, Berlin, 1984. (1984) Zbl0534.49001MR0725856

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