Finite element approximations of Landau-Ginzburg's equation model for structural phase transitions in shape memory alloys
ESAIM: Modélisation mathématique et analyse numérique, Tome 29 (1995) no. 6, pp. 629-655. 
@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: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {629--655},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {29},
     number = {6},
     year = {1995},
     mrnumber = {1360670},
     zbl = {0929.65085},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1995__29_6_629_0/}
}
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: Modélisation mathématique et analyse numérique
PY  - 1995
SP  - 629
EP  - 655
VL  - 29
IS  - 6
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://archive.numdam.org/item/M2AN_1995__29_6_629_0/
LA  - en
ID  - M2AN_1995__29_6_629_0
ER  - 
%0 Journal Article
%A Hoffmann, K.-H.
%A Jun Zou
%T Finite element approximations of Landau-Ginzburg's equation model for structural phase transitions in shape memory alloys
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1995
%P 629-655
%V 29
%N 6
%I AFCET - Gauthier-Villars
%C Paris
%U http://archive.numdam.org/item/M2AN_1995__29_6_629_0/
%G en
%F 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: Modélisation mathématique et analyse numérique, Tome 29 (1995) no. 6, pp. 629-655. http://archive.numdam.org/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

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

[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 | Zbl

[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 | Zbl

[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

[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 | Zbl

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

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

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

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