EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 34 / No 3 (May/june 2000) ESAIM: M2AN, 34 3 (2000) 663-685 References
Free Access
Issue
ESAIM: M2AN
Volume 34, Number 3, May/june 2000
Page(s) 663 - 685
DOI https://doi.org/10.1051/m2an:2000161
Published online 15 April 2002
  1. R. Adams. Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
  2. J. Ball and R. James, Fine phase mixtures as minimizers of energy. Arch. Rat. Mech. Anal. 100 (1987) 13-52. [CrossRef] [MathSciNet] [Google Scholar]
  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. [Google Scholar]
  4. K. Bhattacharya, Self accomodation in martensite. Arch. Rat. Mech. Anal. 120 (1992) 201-244. [CrossRef] [Google Scholar]
  5. K. Bhattacharya and G. Dolzmann, Relaxation of some multiwell problems, in Proc. R. Soc. Edinburgh: Section A, to appear. [Google Scholar]
  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] [Google Scholar]
  7. B. Brighi and M. Chipot, Approximation of infima in the calculus of variations. J. Comput. Appl. Math. 98 (1998) 273-287. [CrossRef] [MathSciNet] [Google Scholar]
  8. C. Carstensen and P. Plechác, Numerical solution of the scalar double-well problem allowing microstructure. Math. Comp., 66 (1997) 997-1026. [Google Scholar]
  9. C. Carstensen and P. Plechác, Adaptive algorithms for scalar non-convex variational problems. Appl. Numer. Math. 26 (1998) 203-216. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Chipot, Numerical analysis of oscillations in nonconvex problems. Numer. Math. 59 (1991) 747-767. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. Chipot and C. Collins, Numerical approximations in variational problems with potential wells. SIAM J. Numer. Anal. 29 (1992) 1002-1019. [CrossRef] [MathSciNet] [Google Scholar]
  12. M. Chipot, C. Collins, and D. Kinderlehrer, Numerical analysis of oscillations in multiple well problems. Numer. Math. 70 (1995) 259-282 . [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Chipot and D. Kinderlehrer, Equilibrium configurations of crystals. Arch. Rat. Mech. Anal. 103 (1988) 237-277. [Google Scholar]
  14. M. Chipot and S. Müller, Sharp energy estimates for finite element approximations of nonconvex problems. (preprint, 1997). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  17. B. Dacorogna, Direct methods in the calculus of variations. Springer-Verlag, Berlin, (1989). [Google Scholar]
  18. G. Dolzmann, Numerical computation of rank-one convex envelopes. SIAM J. Numer. Anal. 36 (1999) 1621-1635. [CrossRef] [MathSciNet] [Google Scholar]
  19. D. French, On the convergence of finite element approximations of a relaxed variational problem. SIAM J. Numer. Anal. 28 (1991) 419-436. [Google Scholar]
  20. L. Jian and R. James, Prediction of microstructure in monoclinic LaNbO4 by energy minimization. Acta Mater. 45 (1997) 4271-4281. [CrossRef] [Google Scholar]
  21. D. Kinderlehrer and P. Pedregal, Characterizations of gradient Young measures. Arch. Rat. Mech. Anal. 115 (1991) 329-365. [Google Scholar]
  22. M. Kruzík, Numerical approach to double well problems. SIAM J. Numer. Anal. 35 (1998) 1833-1849. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  24. B. Li and M. Luskin, Nonconforming finite element approximation of crystalline microstructure. Math. Comp. 67(223) (1998) 917-946. [Google Scholar]
  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] [Google Scholar]
  26. Z. Li, Simultaneous numerical approximation of microstructures and relaxed minimizers. Numer. Math. 78 (1997) 21-38. [CrossRef] [MathSciNet] [Google Scholar]
  27. M. Luskin, Approximation of a laminated microstructure for a rotationally invariant, double well energy density. Numer. Math. 75 (1996) 205-221. [CrossRef] [MathSciNet] [Google Scholar]
  28. M. Luskin, On the computation of crystalline microstructure. Acta Numer. (1996) 191-257. [Google Scholar]
  29. M. Luskin and L. Ma, Analysis of the finite element approximation of microstructure in micromagnetics. SIAM J. Numer. Anal. 29 320-331. [Google Scholar]
  30. R. Nicolaides and N. Walkington, Strong convergence of numerical solutions to degenerate variational problems. Math. Comp. 64 (1995) 117-127. [CrossRef] [MathSciNet] [Google Scholar]
  31. P. Pedregal, Numerical approximation of parametrized measures. Num. Funct. Anal. Opt. 16 (1995) 1049-1066. [CrossRef] [Google Scholar]
  32. P. Pedregal, On the numerical analysis of non-convex variational problems. Numer. Math. 74 (1996) 325-336. [CrossRef] [MathSciNet] [Google Scholar]
  33. T. Roubícek, Numerical approximation of relaxed variational problems. J. Convex Anal. 3 (1996) 329-347. [MathSciNet] [Google Scholar]
  34. N. Simha, Crystallography of the tetragonal → monoclinic transformation in zirconia. J. Phys. IV Colloq. France 5 (1995) C81121-C81126. [Google Scholar]
  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] [Google Scholar]
  36. V. Sverák, Lower-semicontinuity of variational integrals and compensated compactness, in Proceedings ICM 94, Zürich (1995). Birkhäuser. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]

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