@article{M2AN_1999__33_1_67_0,
author = {Li, Bo and Luskin, Mitchell},
title = {Approximation of a martensitic laminate with varying volume fractions},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {33},
year = {1999},
pages = {67-87},
mrnumber = {1685744},
zbl = {0928.74012},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_1999__33_1_67_0}
}
Li, Bo; Luskin, Mitchell. Approximation of a martensitic laminate with varying volume fractions. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 33 (1999) pp. 67-87. http://gdmltest.u-ga.fr/item/M2AN_1999__33_1_67_0/
[1] , Sobolev Spaces. Academic Press, New York (1975). | MR 450957 | Zbl 0314.46030
[2] and , Fine phase mixtures as minimizers of energy. Arch. Rat. Mech. Anal 100 (1987) 13-52. | MR 906132 | Zbl 0629.49020
[3] and , Proposed experimental tests of a theory of fine microstructure and the two-well problem. Phil. Trans. R. Soc.Lond. A 338 (1992) 389-450. | Zbl 0758.73009
[4] and , Experiments on the martensitic transformation in single crystals of indium-thallium alloys.Acta Metall. 2 (1954) 148-166.
[5] and , Diffusionless phase changes in the indium-thallium System. Trans. AIME J. Metals 197 (1953)1516-1524.
[6] and , Numerical solution of the scalar double-well problem allowing microstructure. Math. Comp. 66 (1997) 997-1026. | MR 1415798 | Zbl 0870.65055
[7] , Numerical analysis of oscillations in nonconvex problems. Numer. Math. 59 (1991) 747-767. | MR 1128031 | Zbl 0712.65063
[8] and , Numerical approximations in variational problems with potential wells. SIAM J. Numer. Anal 29 (1992) 1002-1019. | MR 1173182 | Zbl 0763.65049
[9] , and , Numerical analysis of oscillations in multiple well problems. Numer. Math. 70 (1995) 259-282. | MR 1330864 | Zbl 0824.65045
[10] and , Equilibrium configurations of crystals. Arch. Rat Mech. Anal 103 (1988) 237-277. | MR 955934 | Zbl 0673.73012
[11] , The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). | MR 520174 | Zbl 0383.65058
[12] , and , Numerical approximation of the solution of a variational problem with a double well potential. SIAM J. Numer. Anal 28 (1991) 321-332. | MR 1087507 | Zbl 0725.65067
[13] and , Optimal order estimates for the finite element approximation of the solution of a nonconvex variational problem. Math. Comp. 57 (1991) 621-637. | MR 1094944 | Zbl 0735.65042
[14] , Constitutive theory for some constrained elastic crystals. J. Solids and Structures 22 (1986) 951-964. | Zbl 0595.73001
[15] , Stable equilibrium configurations of elastic crystals. Arch. Rat. Mech. Anal. (1986) 1-14. | MR 831767 | Zbl 0597.73006
[16] , On the convergence of finite element approximations of a relaxed variational problem. SIAM J. Numer. Anal. 28, (1991) 419-436. | MR 1043613 | Zbl 0696.65070
[17] , Numerical analysis of a nonconvex variational problem related to solid-solid phase transitions. SIAM J. Numer. Anal. 31 (1994) 111-127. | MR 1259968 | Zbl 0797.65052
[18] , Minimizing sequences and the microstructure of crystals in Proceedings of the-Society of Metals Conference on Phase Transformations. Cambridge University Press (1989).
[19] , Twinning in crystals II. In Metastability and Incompletely Posed Problems. S. Antman, J.L. Ericksen, D. Kinderlehrer and I. Muller Eds. IMA Volumes in Mathematics and Its Applications. Springer-Verlag, New York 3 (1987) 185-212. | MR 870005 | Zbl 0638.73007
[20] and , Characterizations of gradient Young measures. Arch. Rat Mech. Anal 115, (1991) 329-365. | MR 1120852 | Zbl 0754.49020
[21] , Relaxation of a double-well energy. Cont Mech. Thermodyn. 3 (1991) 193-236. | MR 1122017 | Zbl 0825.73029
[22] and , Finite element analysis of microstructure for the cubic to tetragonal transformation. SIAM J. Numer. Anal 35 (1998) 376-392. | MR 1618484 | Zbl 0919.49020
[23] and , Nonconforming finite element approximation of crystalline microstructure. Math. Comp. 67 (1998) 917-946. | MR 1459391 | Zbl 0901.73076
[24] , On the computation of crystalline microstructure. Acta Numerica (1996) 191-257. | MR 1624603 | Zbl 0867.65033
[25] , Approximation of a laminated microstructure for a rotationally invariant, double well energy density. Namer. Math. 75 (1997) 205-221. | MR 1421987 | Zbl 0874.73060
[26] and , Analysis of the finite element approximation of microstructure in micromagnetics. SIAM J. Numer. Anal. 29 (1992) 320-331. | MR 1154269 | Zbl 0760.65113
[27] and , Strong convergence of numerical solutions to degenerate variational problems. Math. Comp. 64 (1995) 117-127. | MR 1262281 | Zbl 0821.65040
[28] , Numerical approximation of parametrized measures. Num. Funct. Anal. Opt. 16, (1995) 1049-1066. | MR 1355286 | Zbl 0848.65049
[29] , On the numerical analysis of non-convex variational problems. Numer. Math. 74 (1996) 325-336. | MR 1408606 | Zbl 0858.65059
[30] and , Numerical Approximation of Partial Differential Equations. Springer-Verlag, Berlin (1994). | MR 1299729 | Zbl 0803.65088
[31] , Numerical approximation of relaxed variational problems. J. Convex Analysis 3, (1996) 329-347. | MR 1448060 | Zbl 0881.65058
[32] , Lower-semicontinuity of variational integrals and compensated compactness in Proceedings ICM 94 Birkhäuser. Zürich (1995). | MR 1404015 | Zbl 0852.49010
[33] , Compensated compactness and applications to partial differential equations in Nonlinear analysis and mechanics. Pitman Research Notes in Mathematics. R. Knops Eds. Pitman, London (1978). | MR 584398 | Zbl 0437.35004
[34] , Partial Differential Equations. Cambridge University Press, Cambridge (1987). | MR 895589 | Zbl 0623.35006