An algorithm for the one-phase Stefan problem

E. Di Benedetto; R. Spigler

Rendiconti del Seminario Matematico della Università di Padova (1983)

  • Volume: 69, page 109-134
  • ISSN: 0041-8994

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Di Benedetto, E., and Spigler, R.. "An algorithm for the one-phase Stefan problem." Rendiconti del Seminario Matematico della Università di Padova 69 (1983): 109-134. <http://eudml.org/doc/107886>.

@article{DiBenedetto1983,
author = {Di Benedetto, E., Spigler, R.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Stefan problem; approximation of the interface free boundary; one- dimensional free boundary problems with change of phase; heat equation; Stefan condition},
language = {eng},
pages = {109-134},
publisher = {Seminario Matematico of the University of Padua},
title = {An algorithm for the one-phase Stefan problem},
url = {http://eudml.org/doc/107886},
volume = {69},
year = {1983},
}

TY - JOUR
AU - Di Benedetto, E.
AU - Spigler, R.
TI - An algorithm for the one-phase Stefan problem
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1983
PB - Seminario Matematico of the University of Padua
VL - 69
SP - 109
EP - 134
LA - eng
KW - Stefan problem; approximation of the interface free boundary; one- dimensional free boundary problems with change of phase; heat equation; Stefan condition
UR - http://eudml.org/doc/107886
ER -

References

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  1. [1] G. Borgioli - E. DIBENEDETTO - M. UGHI, Stefan problems with nonlinear boundary conditions: the polygonal method, Zeit. Angew. Math. Mech., 58 (1978), pp. 539-546. Zbl0398.35037MR524550
  2. [2] J.R. Cannon - J. DOUGLAS, The stability of the boundary in a Stefan problem, Ann. Scuola Norm. Sup. Pisa, 21 (1967), pp. 83-91. Zbl0154.36402MR269998
  3. [3] J.R. Cannon - C. D. HILL, Existence, uniqueness, stability and monotone dependence in a Stefan problem for the heat equation, J. Math. Mech., 17 (1967), pp. 1-20. Zbl0154.36403MR270000
  4. [4] O.A. Ladyzhenskaya - V. A. SOLONNIKOV - N. N. URAL'TSEVA, Linear and quasi-linear equations of parabolic type, Amer. Math. Soc., Trans. of Math. Monographs, 23, Providence, R.I., (1968). Zbl0174.15403
  5. [5] A. Datzeff, Sur le problème linéaire de Stefan, Annuaire Univ. SofiaFac. Sci., 45 (1949), pp. 321-352. MR39161
  6. [6] A. Datzeff, Sur le problème linéaire de Stefan, Memoire de Sciences Physiques, fasc. 69, Gauthiers-Villars, Paris (1970) . 
  7. [7] A. Fasano - M. Primicerio, Il problema di Stefan con condizioni al contorno non lineari, Ann. Scuola Norm. Sup. Pisa, 26 (1972), pp. 711-737. Zbl0245.35048MR366240
  8. [8] A. Fasano - M. Primicerio, Su un problema unidimensionale di diffusione in un mezzo a contorno mobile con condizioni ai limiti non lineari, Ann. Mat. Pura Appl., IV ser., 93 (1972), pp. 333-357. Zbl0277.35055MR410084
  9. [9] A. Fasano - M. Primicerio, La diffusione del calore in uno strato di spessore variabile in presenza di scambi termici con l'ambiente: deduzione di limitazioni a priori sulla temperatura e le sue derivate, Rend. Sem. Mat. Univ. Padova, 50 (1973), pp. 269-330. Zbl0278.35046MR366241
  10. [10] A. Fasano - M. Primicerio, Convergence of Hüber's method for heat conduction problems with change of phase, Zeit. Angew. Math. Mech., 53 (1973), pp. 341-348. Zbl0257.35045MR400930
  11. [11] A. Fasano - M. Primicerio - F. Fontanella, An efficient method for solving free-boundary diffusion problems, Meccanica, 8 (1973), pp. 223-235. MR339691
  12. [12] A. Friedman, Partial differential equations of parabolic type, Prentice Hall, Inc., 1964. Zbl0144.34903MR181836
  13. [13] M. Primicerio, Problemi di diffusione a frontiera libera, Boll. Un. Mat. Ital., (5), 18-A (1981), pp. 11-68. Zbl0468.35082MR607203
  14. [14] J.C.W. Rogers - A.E. Berger - M. Ciment, The alternating phase truncation method for numerical solutions of a Stefan problem, SIAM J. Numer. Anal., 16 (1979), pp. 563-587. Zbl0418.65051MR537272
  15. [15] A. Hüber, Hauptaufsätze über das Fortschreiten der Schmelzgrenze in einem linearen Leiter, Zeit. Angew. Math. Mech., 19 (1939), pp. 1-21. Zbl0021.17301

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