Finite element approximations of Landau-Ginzburg's equation model for structural phase transitions in shape memory alloys

K.-H. Hoffmann; Jun Zou

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1995)

  • Volume: 29, Issue: 6, page 629-655
  • ISSN: 0764-583X

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Hoffmann, K.-H., and Jun Zou. "Finite element approximations of Landau-Ginzburg's equation model for structural phase transitions in shape memory alloys." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 29.6 (1995): 629-655. <http://eudml.org/doc/193786>.

@article{Hoffmann1995,
author = {Hoffmann, K.-H., Jun Zou},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {thermomechanical phase transition; shape memory alloys; error bounds; finite element; Landau-Ginzburg model},
language = {eng},
number = {6},
pages = {629-655},
publisher = {Dunod},
title = {Finite element approximations of Landau-Ginzburg's equation model for structural phase transitions in shape memory alloys},
url = {http://eudml.org/doc/193786},
volume = {29},
year = {1995},
}

TY - JOUR
AU - Hoffmann, K.-H.
AU - Jun Zou
TI - Finite element approximations of Landau-Ginzburg's equation model for structural phase transitions in shape memory alloys
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1995
PB - Dunod
VL - 29
IS - 6
SP - 629
EP - 655
LA - eng
KW - thermomechanical phase transition; shape memory alloys; error bounds; finite element; Landau-Ginzburg model
UR - http://eudml.org/doc/193786
ER -

References

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  1. [1] H. W. ALT, K.-H. HOFFMANN, M. NIEZGODKA and J. SPREKELS, 1985, A numerical study of structural phase transitions in shape memory alloys, Preprint No. 90, University of Augsburg. 
  2. [2] K.-H. HOFFMANN and M. NIEZGODKA, 1990, Mathematical models of dynamical martensitic transformations in shape memory alloys, J. of Intell. Mater. Syst. and Struct., 1, pp. 355-374. 
  3. [3] K.-H. HOFFMANN and JUN ZOU, 1993, The existence and uniqueness of global solutions to a mathematical model for shape memory alloys, Preprint No. 461, DFG-SPP "Anwendungsbezogene Optimierung and Steuerung", Technical University of Munich. Zbl0841.73032MR1360995
  4. [4] D. KINDERLEHRER and G. STAMPACCHIA, 1980, An Introduction to Variational Inequalities and their Applications, New York, Academic Press. Zbl0457.35001MR567696
  5. [5] O. KLEIN, 1993, Stability and uniqueness results for a numerical approximation of the thermomechanical phase transitions in Shape Memory Alloys, Preprint No. 475, DFG-SPP "Anwendungsbezogene Optimierung and Steuerung", University - GH Essen. Zbl0826.65108MR1325961
  6. [6] M. NIEZGODKA and J. SPREKELS, 1991, Convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys, Numer. Math., 58, pp. 759-778. Zbl0715.65099MR1090259
  7. [7] J. SPREKELS, 1990, Shape memory alloy : Mathematical models for a class of first order solid-solid phase transitions in metals, Control and Cybernetics, 19, 1990, 287-308. Zbl1229.49048MR1118688
  8. [8] J. SPREKELS and S. ZHENG, 1989, Global solutions to the equations of a Ginzburg-Landau theory for structural phase transitions in shape memory alloys, Physica, D 39, pp. 59-76. Zbl0696.35145MR1021182
  9. [9] E. STEIN, 1970, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton. Zbl0207.13501MR290095
  10. [10] G. STRANG and G. FIX, 1973, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs. Zbl0356.65096MR443377
  11. [11] G. STRANG, 1972, Approximation in the finite element method, Numer. Math., 19, pp. 81-98. Zbl0221.65174MR305547
  12. [12] T. TIIHONEN, 1988, A numerical approach to a shape memory model, Preprint No. 98, DFG-SPP "Anwendungsbezogene Optimierung und Steuerung", University of Augsburg. 

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