Free Access
Issue
ESAIM: M2AN
Volume 35, Number 5, September-October 2001
Page(s) 865 - 878
DOI https://doi.org/10.1051/m2an:2001139
Published online 15 April 2002
  1. J.M. Ball and R.D. James, Fine phase mixtures as minimisers of energy. Arch. Rational Mech. Anal. 100 (1987) 13-52. [Google Scholar]
  2. J.M. Ball and R.D. James, Proposed experimental tests of the theory of fine microstructure and the two-well problem. Philos. Trans. Roy. Soc. London Ser. A 338 (1992) 389-450. [Google Scholar]
  3. M. Bildhauer, M. Fuchs and G. Seregin, Local regularity of solutions of variational problems for the equilibrium configuration of an incompressible, multiphase elastic body. Nonlin. Diff. Equations Appl. 8 (2001) 53-81. [CrossRef] [Google Scholar]
  4. S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods, in Texts in Applied Mathematics 15. Springer-Verlag, New York (1994). [Google Scholar]
  5. C. Carstensen and S. A. Funken, Constants in Clément-interpolation error and residual based a posteriori estimates in finite element methods. East-West J. Numer. Math. 8 (2000) 153-175. [MathSciNet] [Google Scholar]
  6. C. Carstensen and S. A. Funken, Fully reliable localised error control in the FEM. SIAM J. Sci. Comput. 21 (2000) 1465-1484. [Google Scholar]
  7. C. Carstensen and S. Müller, Local stress regularity in scalar non-convex variational problems. In preparation. [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 Petr Plechác, Numerical analysis of compatible phase transitions in elastic solids. SIAM J. Numer. Anal. 37 (2000) 2061-2081. [CrossRef] [MathSciNet] [Google Scholar]
  10. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland Publishing Company, Amsterdam, New York, Oxford (1978). [Google Scholar]
  11. H. Le Dret and A. Raoult, Variational convergence for nonlinear shell models with directors and related semicontinuity and relaxation results. Arch. Rational Mech. Anal. 154 (1999) 101-134. [Google Scholar]
  12. K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Introduction to adaptive methods for differential equations, in Acta Numerica, A. Iserles, Ed., Cambridge University Press, Cambridge (1995) 105-158. [Google Scholar]
  13. I. Fonseca and S. Müller, A-quasiconvexity, lower semicontinuity and Young measures. SIAM J. Math. Anal. 30 (1999) 1355-1390. [CrossRef] [MathSciNet] [Google Scholar]
  14. J. Goodman, R.V. Kohn and L. Reyna, Numerical study of a relaxed variational problem from optimal design. Comput. Methods Appl. Mech. Engrg. 57 (1986) 107-127. [CrossRef] [MathSciNet] [Google Scholar]
  15. A. G. Khachaturyan, Theory of Structural Transformations in Solids. John Wiley & Sons, New York (1983). [Google Scholar]
  16. M.S. Kuczma, A. Mielke and E. Stein, Modelling of hysteresis in two-phase systems. Solid Mechanics Conference (1999); Arch. Mech. 51 (1999) 693-715. [Google Scholar]
  17. R.V. Kohn, The relaxation of a double-well energy. Contin. Mech. Thermodyn. 3 (1991) 193-236. [Google Scholar]
  18. M. Luskin, On the computation of crystalline microstructure, in Acta Numerica, A. Iserles, Ed., Cambridge University Press, Cambridge (1996) 191-257. [Google Scholar]
  19. A. Mielke and F. Theil, A mathematical model for rate-independent phase transformations with hysteresis, in Workshop of Continuum Mechanics in Analysis and Engineering, H.-D. Alber, D. Bateau and R. Farwig, Eds. , Shaker-Verlag, Aachen (1999) 117-129. [Google Scholar]
  20. A. Mielke, F. Theil and V. I. Levitas, A variational formulation of rate-independent phase transformations using an extremum principle. Submitted to Arch. Rational Mech. Anal. [Google Scholar]
  21. A. L. Roitburd, Martensitic transformation as a typical phase transformation in solids, in Solid State Physics 33, Academic Press, New York (1978) 317-390. [Google Scholar]
  22. G.A. Seregin, The regularity properties of solutions of variational problems in the theory of phase transitions in an elastic body. St. Petersbg. Math. J. 7 (1996) 979-1003, English translation from Algebra Anal. 7 (1995) 153-187. [Google Scholar]
  23. R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques, in Wiley-Teubner Series Advances in Numerical Mathematics, John Wiley & Sons, Chichester; Teubner, Stuttgart (1996). [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