Error estimates and free-boundary convergence for a finite difference discretization of a parabolic variational inequality
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 11 (1977) no. 4, p. 315-340
@article{M2AN_1977__11_4_315_0,
     author = {Baiocchi, Claudio and Pozzi, G. A.},
     title = {Error estimates and free-boundary convergence for a finite difference discretization of a parabolic variational inequality},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {11},
     number = {4},
     year = {1977},
     pages = {315-340},
     zbl = {0371.65020},
     mrnumber = {464607},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1977__11_4_315_0}
}
Baiocchi, C.; Pozzi, G. A. Error estimates and free-boundary convergence for a finite difference discretization of a parabolic variational inequality. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 11 (1977) no. 4, pp. 315-340. http://www.numdam.org/item/M2AN_1977__11_4_315_0/

1. C. Baiocchi and G. A. Pozzi, An évolution variational inequality related toa diffusion-absorption problem, , Appl. Math, and Optim., 2, 1975-1976, pp. 304-314 | MR 430538 | Zbl 0379.49014

2. A. E. Berger, The truncation method for the solution of a class of variationalinequalities, R.A.I.R.O. Anal. Numér., 10, 1976, pp. 29-42. | Numdam | MR 455489 | Zbl 0334.49012

3. A. E. Berger, M. Ciment and J. C. W. Rogers, Numerical solution ofa diffusionconsumption problem with a free boundary, S.I.A.M. Journ. Num. Anal., 12, 1975, pp. 646-672. | MR 383779 | Zbl 0317.65032

4. H. Brezis, Solutions with compact support of variational inequalities, Uspehi Mat. Nauk SSSR, Vol. 29, 2, 1974, pp. 103-106; English translation: Russian Math, Surveys, Vol. 29, 2, 1974, pp. 103-108. | MR 481460 | Zbl 0304.35036

5. H. Brezis and A. Friedman, Estimates on the support of solution of parabolic variational inequalities, Illinois J. Math., Vol. 20, 1976, pp. 82-97. | MR 390501 | Zbl 0316.35046

6. J. Crank, The Mathematics of Diffusion, 2nd éd., Clarendon Press, Oxford, 1975. | MR 359551 | Zbl 0427.35035

7. J. J. Crank and R. S. Gupta, A moving boundary problem arising from diffusion of oxygen in absorbing tissue, J. Inst. Math. Appl., Vol. 10, 1972, pp. 19-33. | MR 347105 | Zbl 0247.65064

8. J. Crank and R. S. Gupta, A method for solving moving boundary problems in heat flow using cubic splines or polynomials, J. Inst. Math. Appl., Vol. 10, 1972, pp. 296-304. | MR 347105 | Zbl 0299.65049

9. G. Duvaut, Problèmes à frontière libre en théorie des milieux continus, I.R.I.A., Rapport de Recherche N° 185, 1976.

10. G. Duvaut and J. L. Lions, Les Inéquations en Mécanique et en Physique, Dunod, Paris, 1972; English transi.: Springer, Berlin, 1975. | MR 464857 | Zbl 0298.73001

11. A. Fasano and M. Primicerio, General free-boundary problems for the heat equations; parts I, II, III, J. Math. Anal, and Appl., 57, 1977, pp. 694-723;58, 1977, pp. 202-231; 59, 1977, pp. 1-14. | MR 487017 | Zbl 0355.35037

12. A. Friedman, Parabolic variational inequalities in one space dimension and smoothness of the free boundary, J. Funct. Anal., Vol. 18, 1975, pp. 151-176. | MR 477461 | Zbl 0295.35045

13. E. Hansen and P. Hougaard, Ona moving boundary problem from biomechanic, J. Inst. Maths. Appls, Vol. 13, 1974, pp. 385-398. | Zbl 0307.45016

14. J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod and Gauthier-Villars, Paris, 1969. | MR 259693 | Zbl 0189.40603

15. J. L. Lions and E. Magenes, Problèmes aux limites non homogènes, Vol.I, II,III, Dunod, Paris, 1968-1970; English transi.: Springer, Berlin, 1972.

16. J. L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl.Math., Vol. 20, 1967, pp. 493-519. | MR 216344 | Zbl 0152.34601

17. E. Magenes, Topics in parabolic equations: some typical free boundary problems. Proc. of N.A.T.O. Advanced Study Inst. on Boundary value problems for evolution partial differential equations, Liège, September 1976. | MR 470497 | Zbl 0366.35001

18. M. Primicerio, Problemi a contorno liberoper equazioni délia diffusione, Rend.Sem. Mat. Torino, 32, 1973-1974, pp. 183-206. | MR 477466 | Zbl 0307.76048

19. A. Schatz, Free boundary problems of Stefan type with prescribed flux, J. Math.Anal. Appl., Vol. 28, 1969, pp. 569-580. | MR 267285 | Zbl 0271.35038