Free access
Issue
ESAIM: M2AN
Volume 36, Number 4, July/August 2002
Page(s) 573 - 595
DOI http://dx.doi.org/10.1051/m2an:2002026
Published online 15 September 2002
  1. V. Alexiades and A.D. Solomon, Mathematical modeling of melting and freezing processes. Hemisphere Publishing Corporation, Washington (1993).
  2. H. Amann, Ordinary differential equations. An introduction to nonlinear analysis, Vol. 13 of De Gruyter Studies in Mathematics. Walter de Gruyter, Berlin (1990).
  3. E. Bänsch and A. Schmidt, A finite element method for dendritic growth, in Computational crystal growers workshop, J.E. Taylor Ed., AMS Selected Lectures in Mathematics (1992) 16-20.
  4. X. Chen, J. Hong and F. Yi, Existence, uniqueness, and regularity of classical solutions of the Mullins-Sekerka problem. Comm. Partial Differential Equations 21 (1996) 1705-1727. [MathSciNet]
  5. K. Deckelnick and G. Dziuk, Convergence of a finite element method for non-parametric mean curvature flow. Numer. Math. 72 (1995) 197-222. [CrossRef] [MathSciNet]
  6. J. Escher and G. Simonett, Classical solutions for Hele-Shaw models with surface tension. Adv. Differential Equations 2 (1997) 619-642. [MathSciNet]
  7. J. Escher and G. Simonett, Classical solutions for the quasi-stationary Stefan problem with surface tension, in Papers associated with the international conference on partial differential equations, Potsdam, Germany, June 29-July 2, 1996, M. Demuth et al. Eds., Vol. 100. Akademie Verlag, Math. Res., Berlin (1997) 98-104.
  8. L.C. Evans and R. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, Inc., 2000 Corporate Blvd., N.W., Boca Ratin, Stud. Adv. Math., 33431, Florida (1992).
  9. M. Fried, A level set based finite element algorithm for the simulation of dendritic growth. Submitted to Computing and Visualization in Science, Springer.
  10. M.E. Gurtin, Thermomechanics of evolving phase boundaries in the plane. Clarendon Press, Oxford (1993).
  11. J.S. Langer, Instabilities and pattern formation in crystal growth. Rev. Modern Phys. 52 (1980) 1-28. [CrossRef]
  12. W.W. Mullins and R.F. Sekerka, Stability of a planar interface during solidification of a dilute binary alloy. J. Appl. Phys. 35 (1964) 444-451. [CrossRef]
  13. L. Perko, Differential equations and dynamical systems. 2nd ed, Vol. 7 of Texts in Applied Mathematics. Springer, New York (1996).
  14. A. Schmidt, Computation of three dimensional dendrites with finite elements. J. Comput. Phys. 125 (1996) 293-312. [CrossRef]
  15. R.F. Sekerka, Morphological instabilities during phase transformations, in Phase transformations and material instabilities in solids, Proc. Conf., Madison/Wis. 1983. Madison 52, M. Gurtin Ed., Publ. Math. Res. Cent. Univ. Wis. (1984) 147-162.
  16. J. Strain, Velocity effects in unstable solidification. SIAM J. Appl. Math. 50 (1990) 1-15. [CrossRef] [MathSciNet]
  17. G. Strang and G.J. Fix, An analysis of the finite element method. Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J (1973).
  18. A. Veeser, Error estimates for semi-discrete dendritic growth. Interfaces Free Bound. 1 (1999) 227-255. [CrossRef] [MathSciNet]
  19. A. Visintin, Models of phase transitions, Vol. 28 of Progress in Nonlinear Differential Equations and Their Applications. Birkhäuser, Boston (1996).
  20. W.P. Ziemer, Weakly Differentiable Functions, Vol. 120 of Graduate Texts in Mathematics. Springer-Verlag, New York (1989).

Recommended for you