Free Access
Issue
ESAIM: M2AN
Volume 20, Number 2, 1986
Page(s) 355 - 368
DOI https://doi.org/10.1051/m2an/1986200203551
Published online 31 January 2017
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  3. C BAIOCCHI, G POZZI, Error estimates and free-boundary convergence for a finite difference discretization of a parabolic variational inequality, RAIRO Numer Anal 11, 4 (1977), pp 315-340 [EuDML: 193305] [MR: 464607] [Zbl: 0371.65020]
  4. H BREZIS, Seuil de régulante pour certains problèmes unilatéraux, C R Acad Sci Paris 273 (1971), pp 35-37 [MR: 287366] [Zbl: 0214.10703]
  5. H BREZIS, D KINDERLEHRER, The smoothness of solutions to nonlinear variational inequahties Indiana Univ Math J 23, 9 (1974), pp 831-844 [MR: 361436] [Zbl: 0278.49011]
  6. F BREZZI, L CAFFARELLI, Convergence of the discrete free boundaries for finite element approximations, RAIRO Numer Anal 17 (1983), pp 385-395 [EuDML: 193422] [MR: 713766] [Zbl: 0547.65081]
  7. F BREZZI, W HAGER, P RAVIART, Error estimates for the finite element solution of variational inequahties Part I Primal Theory, Numer Math 28 (1977), pp 431-443 [EuDML: 132496] [MR: 448949] [Zbl: 0369.65030]
  8. F BREZZI, W HAGER, P RAVIART, Error estimates for the finite element solution of variational inequalities Part II Mixed Methods, Numer Math 31 (1978), pp 1-16 [EuDML: 132563] [MR: 508584] [Zbl: 0427.65077]
  9. F BREZZI, G SACCHI, A finite element approximation of a variational inequality related to hydraulics, Calcolo 13, III (1976), pp. 257-274 [MR: 520171] [Zbl: 0353.76068]
  10. L CAFFARELLI, A remark on the Hausdorff measure of a free boundary, and the convergence of coincidence sets, Boll U M I (1981), pp. 109-113 [MR: 607212] [Zbl: 0453.35085]
  11. L CAFFARELLI, L EVANS, Continuity of the temperature in the two-phase Stefan problems Arch Rational Mech Anal 81, 3 (1983), pp 199-220 [MR: 683353] [Zbl: 0516.35080]
  12. L CAFFARELLI, A FRIEDMAN, Regularity of the free boundary for the one dimensional flow of gas in a porous medium, Amer J Math (1979), pp 1193-1218 [MR: 548877] [Zbl: 0439.76084]
  13. L CAFFARELLI, A FRIEDMAN, Regularity of the free boundary of a gas flow in an n-dimensional porous medium, Indiana Univ Math J 29 (1980), pp 361-391 [MR: 570687] [Zbl: 0439.76085]
  14. L CAFFARELLI, N RIVIÈRE, Asymptotic behavior of free boundaries at their singular points, Ann Math 106 (1977), pp 309-317 [MR: 463690] [Zbl: 0364.35041]
  15. P CIARLET, The finite element method for elliptic problems, North-Holland (1978) [MR: 520174] [Zbl: 0383.65058]
  16. P CIARLET, P RAVIART, Maximum principle and uniform convergence for the finite element method, Comput Methods Appl Mech Engrg 2 (1973), pp 17-31 [MR: 375802] [Zbl: 0251.65069]
  17. A DAMLAMIAN, Some results in the multiphase Stefan problem, Comm Partial Differential Equations 2, 10 (1977), pp 1017-1044 [MR: 487015] [Zbl: 0399.35054]
  18. E DI BENEDETTO, Continuity of weak-solutions to certain singular parabolic equations Ann Mat Pura Appl IV, 130 (1982), pp 131-176 [MR: 663969] [Zbl: 0503.35018]
  19. A boundary modulus of continuity for a class of singular parabolic equations (to appear) [Zbl: 0606.35044]
  20. A FRIEDMAN,, The Stefan problem in several space variables, Trans Amer Math Soc 133 (1968), pp 51-87 [MR: 227625] [Zbl: 0162.41903]
  21. A FRIEDMAN, Variational Principles and Free-Boundary Problems, John Wiley & Sons (1982) [MR: 679313] [Zbl: 0564.49002]
  22. L JEROME, M ROSE, Error estimetes for the multidimensional two-phase Stefan problem, Math Comp 39, 160 (1982), pp 377-414 [MR: 669635] [Zbl: 0505.65060]
  23. B KNERR, The porous medium equation in one dimension, Trans Amer Math Soc 234 (1977), pp 381-415 [MR: 492856] [Zbl: 0365.35030]
  24. M NIEZGODKA, I PAWLOW, A generalized Stefan problem in several space variables Appl Math Optim 9 (1983), pp 193-224 [MR: 687720] [Zbl: 0519.35079]
  25. J NITSCHE, $L_\infty $-convergence of finite element approximations, Mathematical Aspects of F E M, Lectures Notes m Math 606, Springer (1977), pp 261-274 [MR: 488848] [Zbl: 0362.65088]
  26. R NOCHETTO, Error estimates for two-phase Stefan problems in several space variables, I linear boundary conditions, II non-linear flux conditions (to appear in Calcolo) [MR: 859087] [Zbl: 0606.65084]
  27. R NOCHETTO, Error estimates for multidimensional Stefan problems with general boundary conditions Free boundary problems applications and theory, Vol III (A Bossavitera/ eds ), Res Notes Math 120, Pitman (1985), pp 50-60 [MR: 863161] [Zbl: 0593.35094]
  28. R NOCHETTO, A class of non-degenerate two-phase Stefan problems in several space variables, Pubblicazione N° 442 del I A N di Pavia (1984) (to appear in Comm Partial Differential Equations) [MR: 869101] [Zbl: 0624.35085]
  29. P PIETRA, C VERDI, Convergence of the approximate free-boundary for the multidimensional one-phase Stefan problem, Pubblicazione N° 440 del I A N di Pavia (1984) (to appear in Comp Mech Int J ) [Zbl: 0622.65126]
  30. R RANNACHER, R SCOTT, Some optimal error estimates for piecewise linear finite element approximations Math Comp 38, 158 (1982), pp 437-445 [MR: 645661] [Zbl: 0483.65007]
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  32. A VISINTIN, Sur le problème de Stefan avec flux non lineaire, Boll U M I , Anal Funz e Appl, V, 18 C, 1 (1981), pp 63-86 [MR: 631569] [Zbl: 0471.35078]

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