Error estimates and free-boundary convergence for a finite difference discretization of a parabolic variational inequality

 Access to full text

 Full (PDF)

1. 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 Zbl0379.49014MR430538
2. 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. Zbl0334.49012MR455489
3. 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. Zbl0317.65032MR383779
4. 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. Zbl0304.35036MR481460
5. 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. Zbl0316.35046MR390501
6. 6. J. CRANK, The Mathematics of Diffusion, 2nd éd., Clarendon Press, Oxford, 1975. Zbl0427.35035MR359551
7. 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. Zbl0247.65064MR347105
8. 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. Zbl0299.65049MR347105
9. 9. G. DUVAUT, Problèmes à frontière libre en théorie des milieux continus, I.R.I.A., Rapport de Recherche N° 185, 1976. 
10. 10. G. DUVAUT and J. L. LIONS, Les Inéquations en Mécanique et en Physique, Dunod, Paris, 1972; English transi.: Springer, Berlin, 1975. Zbl0298.73001MR464857
11. 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. Zbl0355.35037MR487017
12. 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. Zbl0295.35045MR477461
13. 13. E. HANSEN and P. HOUGAARD, Ona moving boundary problem from biomechanic, J. Inst. Maths. Appls, Vol. 13, 1974, pp. 385-398. Zbl0307.45016
14. 14. J. L. LIONS, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod and Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
15. 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. Zbl0165.10801
16. 16. J. L. LIONS and G. STAMPACCHIA, Variational inequalities, Comm. Pure Appl.Math., Vol. 20, 1967, pp. 493-519. Zbl0152.34601MR216344
17. 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. Zbl0366.35001MR470497
18. 18. M. PRIMICERIO, Problemi a contorno liberoper equazioni délia diffusione, Rend.Sem. Mat. Torino, 32, 1973-1974, pp. 183-206. Zbl0307.76048MR477466
19. 19. A. SCHATZ, Free boundary problems of Stefan type with prescribed flux, J. Math.Anal. Appl., Vol. 28, 1969, pp. 569-580. Zbl0271.35038MR267285

1. Vlad Bally, Bruno Saussereau, Approximation of the Snell envelope and american options prices in dimension one
2. Vlad Bally, Bruno Saussereau, Approximation of the Snell Envelope and American Options Prices in dimension one
3. Ricardo H. Nochetto, A note on the approximation of free boundaries by finite element methods
4. Stefano Finzi Vita, $L_{\infty }$-error estimates for variational inequalities with Hölder continuous obstacle
5. Philippe Cortey-Dumont, Approximation numérique d'une inéquation quasi variationnelle liée à des problèmes de gestion de stock