Free Access
Volume 34, Number 3, May/june 2000
Page(s) 663 - 685
Published online 15 April 2002
  1. R. Adams. Sobolev Spaces. Academic Press, New York (1975).
  2. J. Ball and R. James, Fine phase mixtures as minimizers of energy. Arch. Rat. Mech. Anal. 100 (1987) 13-52. [CrossRef] [MathSciNet]
  3. J. Ball and R. James, Proposed experimental tests of a theory of fine microstructure and the two-well problem. Phil. Trans. R. Soc. Lond. A 338 (1992) 389-450. [CrossRef]
  4. K. Bhattacharya, Self accomodation in martensite. Arch. Rat. Mech. Anal. 120 (1992) 201-244. [CrossRef]
  5. K. Bhattacharya and G. Dolzmann, Relaxation of some multiwell problems, in Proc. R. Soc. Edinburgh: Section A, to appear.
  6. K. Bhattacharya, B. Li and M. Luskin, The simply laminated microstructure in martensitic crystals that undergo a cubic to orthorhombic phase transformation. Arch. Rat. Mech. Anal. 149 (2000) 123-154. [CrossRef]
  7. B. Brighi and M. Chipot, Approximation of infima in the calculus of variations. J. Comput. Appl. Math. 98 (1998) 273-287. [CrossRef] [MathSciNet]
  8. C. Carstensen and P. Plechác, Numerical solution of the scalar double-well problem allowing microstructure. Math. Comp., 66 (1997) 997-1026. [CrossRef] [MathSciNet]
  9. C. Carstensen and P. Plechác, Adaptive algorithms for scalar non-convex variational problems. Appl. Numer. Math. 26 (1998) 203-216. [CrossRef] [MathSciNet]
  10. M. Chipot, Numerical analysis of oscillations in nonconvex problems. Numer. Math. 59 (1991) 747-767. [CrossRef] [MathSciNet]
  11. M. Chipot and C. Collins, Numerical approximations in variational problems with potential wells. SIAM J. Numer. Anal. 29 (1992) 1002-1019. [CrossRef] [MathSciNet]
  12. M. Chipot, C. Collins, and D. Kinderlehrer, Numerical analysis of oscillations in multiple well problems. Numer. Math. 70 (1995) 259-282 . [CrossRef] [MathSciNet]
  13. M. Chipot and D. Kinderlehrer, Equilibrium configurations of crystals. Arch. Rat. Mech. Anal. 103 (1988) 237-277.
  14. M. Chipot and S. Müller, Sharp energy estimates for finite element approximations of nonconvex problems. (preprint, 1997).
  15. C. Collins, D. Kinderlehrer, and M. Luskin, Numerical approximation of the solution of a variational problem with a double well potential. SIAM J. Numer. Anal. 28 (1991) 321-332. [CrossRef] [MathSciNet]
  16. C. Collins and M. Luskin, Optimal order estimates for the finite element approximation of the solution of a nonconvex variational problem. Math. Comp. 57 (1991) 621-637. [CrossRef] [MathSciNet]
  17. B. Dacorogna, Direct methods in the calculus of variations. Springer-Verlag, Berlin, (1989).
  18. G. Dolzmann, Numerical computation of rank-one convex envelopes. SIAM J. Numer. Anal. 36 (1999) 1621-1635. [CrossRef] [MathSciNet]
  19. D. French, On the convergence of finite element approximations of a relaxed variational problem. SIAM J. Numer. Anal. 28 (1991) 419-436.
  20. L. Jian and R. James, Prediction of microstructure in monoclinic LaNbO4 by energy minimization. Acta Mater. 45 (1997) 4271-4281. [CrossRef]
  21. D. Kinderlehrer and P. Pedregal, Characterizations of gradient Young measures. Arch. Rat. Mech. Anal. 115 (1991) 329-365. [CrossRef] [MathSciNet]
  22. M. Kruzík, Numerical approach to double well problems. SIAM J. Numer. Anal. 35 (1998) 1833-1849. [CrossRef] [MathSciNet]
  23. B. Li and M. Luskin, Finite element analysis of microstructure for the cubic to tetragonal transformation. SIAM J. Numer. Anal. 35 (1998) 376-392. [CrossRef] [MathSciNet]
  24. B. Li and M. Luskin, Nonconforming finite element approximation of crystalline microstructure. Math. Comp. 67(223) (1998) 917-946.
  25. B. Li and M. Luskin, Approximation of a martensitic laminate with varying volume fractions. Math. Model. Numer. Anal. 33 (1999) 67-87. [CrossRef] [EDP Sciences] [MathSciNet]
  26. Z. Li, Simultaneous numerical approximation of microstructures and relaxed minimizers. Numer. Math. 78 (1997) 21-38. [CrossRef] [MathSciNet]
  27. M. Luskin, Approximation of a laminated microstructure for a rotationally invariant, double well energy density. Numer. Math. 75 (1996) 205-221. [CrossRef] [MathSciNet]
  28. M. Luskin, On the computation of crystalline microstructure. Acta Numer. (1996) 191-257.
  29. M. Luskin and L. Ma, Analysis of the finite element approximation of microstructure in micromagnetics. SIAM J. Numer. Anal. 29 320-331.
  30. R. Nicolaides and N. Walkington, Strong convergence of numerical solutions to degenerate variational problems. Math. Comp. 64 (1995) 117-127. [CrossRef] [MathSciNet]
  31. P. Pedregal, Numerical approximation of parametrized measures. Num. Funct. Anal. Opt. 16 (1995) 1049-1066. [CrossRef]
  32. P. Pedregal, On the numerical analysis of non-convex variational problems. Numer. Math. 74 (1996) 325-336. [CrossRef] [MathSciNet]
  33. T. Roubícek, Numerical approximation of relaxed variational problems. J. Convex Anal. 3 (1996) 329-347. [MathSciNet]
  34. N. Simha, Crystallography of the tetragonal → monoclinic transformation in zirconia. J. Phys. IV Colloq. France 5 (1995) C81121-C81126.
  35. N. Simha, Twin and habit plane microstructures due to the tetragonal to monoclinic transformation of zirconia. J. Mech. Phys. Solids 45 (1997) 261-292. [CrossRef]
  36. V. Sverák, Lower-semicontinuity of variational integrals and compensated compactness, in Proceedings ICM 94, Zürich (1995). Birkhäuser.
  37. L. Tartar, Compensated compactness and applications to partial differential equations, in: Nonlinear analysis and mechanics, R. Knops, Ed., Pitman Research Notes in Mathematics, London 39 (1978) 136-212.
  38. G. Zanzotto, Twinning in minerals and metals: remarks on the comparison of a thermoelasticity theory with some available experimental results. Atti Acc. Lincei Rend. Fis. 82 (1988) 725-756.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you