Finite element approximations of Landau-Ginzburg's equation model for structural phase transitions in shape memory alloys
Hoffmann, K.-H. ; Jun Zou
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 29 (1995), p. 629-655 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{M2AN_1995__29_6_629_0,
     author = {Hoffmann, K.-H. and Jun Zou},
     title = {Finite element approximations of Landau-Ginzburg's equation model for structural phase transitions in shape memory alloys},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {29},
     year = {1995},
     pages = {629-655},
     mrnumber = {1360670},
     zbl = {0929.65085},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1995__29_6_629_0}
}

Hoffmann, K.-H.; 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, Tome 29 (1995) pp. 629-655. http://gdmltest.u-ga.fr/item/M2AN_1995__29_6_629_0/

[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] 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] 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. | MR 1360995

[4] D. Kinderlehrer and G. Stampacchia, 1980, An Introduction to Variational Inequalities and their Applications, New York, Academic Press. | MR 567696 | Zbl 0457.35001

[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. | MR 1325961 | Zbl 0826.65108

[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. | MR 1090259 | Zbl 0715.65099

[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. | MR 1118688

[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. | MR 1021182 | Zbl 0696.35145

[9] E. Stein, 1970, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton. | MR 290095 | Zbl 0207.13501

[10] G. Strang and G. Fix, 1973, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs. | MR 443377 | Zbl 0356.65096

[11] G. Strang, 1972, Approximation in the finite element method, Numer. Math., 19, pp. 81-98. | MR 305547 | Zbl 0221.65174

[12] T. Tiihonen, 1988, A numerical approach to a shape memory model, Preprint No. 98, DFG-SPP "Anwendungsbezogene Optimierung und Steuerung", University of Augsburg.