On the Convergence of the Approximate Free Boundary for the Parabolic Obstacle Problem
Pietra, Paola ; Verdi, Claudio
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 78 (1985), p. 159-171 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

Si discretizza il problema dell'ostacolo parabolico con differenze all'indietro nel tempo ed elementi finiti lineari nello spazio e si dimostrano stime dell'errore per la frontiera libera discreta.

Publié le : 1985-12-01
@article{RLINA_1985_8_79_6_159_0,
     author = {Paola Pietra and Claudio Verdi},
     title = {On the Convergence of the Approximate Free Boundary for the Parabolic Obstacle Problem},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
     volume = {78},
     year = {1985},
     pages = {159-171},
     zbl = {0635.65128},
     mrnumber = {0944369},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLINA_1985_8_79_6_159_0}
}

Pietra, Paola; Verdi, Claudio. On the Convergence of the Approximate Free Boundary for the Parabolic Obstacle Problem. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 78 (1985) pp. 159-171. http://gdmltest.u-ga.fr/item/RLINA_1985_8_79_6_159_0/

[1] Brezzi, F. and Caffarelli, L.A. (1983) - Convergence of the discrete free boundaries for finite element approximations, «R.A.I.R.O. Anal. Numér.», 17, 385-395. | MR 713766 | Zbl 0547.65081

[2] Caffarelli, L.A. (1981) — A remark on the Hausdorff measure of a free boundary and the convergence of coincidence sets, «Boll. U.M.I.», (5) 18-A, 109-113. | MR 607212 | Zbl 0453.35085

[3] Ciarlet, P.G. (1971) - Fonction de Green discrètes et principe du maximum discret, Thesis Univ. Paris VI.

[4] Ciarlet, P.G. (1978) - The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam. | MR 520174 | Zbl 0383.65058

[5] Ciarlet, P.G. and Raviart, P.A. (1973) - Maximum principle and uniform convergence for the finite element method, «Comput. Meth. Appl. Engrg.», 2, 17-31. | MR 375802 | Zbl 0251.65069

[6] Cortey Dumont, Ph. - On finite element approximation in the L∞-norm of parabolic obstacle variational inequalities and quasi-variational inequalities, preprint. | Zbl 0574.65064

[7] Federer, H. (1969) - Geometric Measure Theory, Springer, Berlin. | MR 257325 | Zbl 0176.00801

[8] Friedman, A. (1982) - Variational Principles and Free Boundary Problems, Wiley, New York. | MR 679313 | Zbl 0564.49002

[9] Glowinski, R., Lions, J.L. and Tremolieres, R. (1981) - Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam. | MR 635927 | Zbl 0463.65046

[10] R.H. NOCHETTO - A note on the approximation of free boundaries by finite element methods, to appear in M2⁢A⁢N (ex «R.A.I.R.O. Anal. Numér.»). | MR 852686 | Zbl 0596.65092

[11] Pietra, P. and Verdi, C. - Convergence of the approximate free boundary for the multidimensional one-phase Stefan problem, to appear in «Comp. Mech.». | Zbl 0622.65126

[12] Fetter, A. - L∞-error estimate for an approximation of a parabolic variational inequality, preprint. | MR 880335 | Zbl 0617.65064