On the Convergence of the Approximate Free Boundary for the Parabolic Obstacle Problem

Paola Pietra; Claudio Verdi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1985)

  • Volume: 79, Issue: 6, page 159-171
  • ISSN: 0392-7881

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Pietra, Paola, and 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 79.6 (1985): 159-171. <http://eudml.org/doc/289256>.

@article{Pietra1985,
author = {Pietra, Paola, Verdi, Claudio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {eng},
month = {12},
number = {6},
pages = {159-171},
publisher = {Accademia Nazionale dei Lincei},
title = {On the Convergence of the Approximate Free Boundary for the Parabolic Obstacle Problem},
url = {http://eudml.org/doc/289256},
volume = {79},
year = {1985},
}

TY - JOUR
AU - Pietra, Paola
AU - Verdi, Claudio
TI - On the Convergence of the Approximate Free Boundary for the Parabolic Obstacle Problem
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1985/12//
PB - Accademia Nazionale dei Lincei
VL - 79
IS - 6
SP - 159
EP - 171
LA - eng
UR - http://eudml.org/doc/289256
ER -

References

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  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. Zbl0547.65081MR713766
  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. Zbl0453.35085MR607212
  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. Zbl0383.65058MR520174
  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. Zbl0251.65069MR375802
  6. CORTEY DUMONT, PH. - On finite element approximation in the L ∞ -norm of parabolic obstacle variational inequalities and quasi-variational inequalities, preprint. Zbl0574.65064
  7. FEDERER, H. (1969) - Geometric Measure Theory, Springer, Berlin. Zbl0176.00801MR257325
  8. FRIEDMAN, A. (1982) - Variational Principles and Free Boundary Problems, Wiley, New York. Zbl0564.49002MR679313
  9. GLOWINSKI, R., LIONS, J.L. and TREMOLIERES, R. (1981) - Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam. Zbl0463.65046MR635927
  10. R.H. NOCHETTO - A note on the approximation of free boundaries by finite element methods, to appear in M 2 ⁢ A ⁢ N (ex «R.A.I.R.O. Anal. Numér.»). Zbl0596.65092MR852686
  11. PIETRA, P. and VERDI, C. - Convergence of the approximate free boundary for the multidimensional one-phase Stefan problem, to appear in «Comp. Mech.». Zbl0622.65126
  12. FETTER, A. - L ∞ -error estimate for an approximation of a parabolic variational inequality, preprint. Zbl0617.65064MR880335DOI10.1007/BF01408576

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