A note on the approximation of free boundaries by finite element methods
ESAIM: Modélisation mathématique et analyse numérique, Volume 20 (1986) no. 2, pp. 355-368.
@article{M2AN_1986__20_2_355_0,
     author = {Nochetto, Ricardo H.},
     title = {A note on the approximation of free boundaries by finite element methods},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {355--368},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {20},
     number = {2},
     year = {1986},
     mrnumber = {852686},
     zbl = {0596.65092},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1986__20_2_355_0/}
}
TY  - JOUR
AU  - Nochetto, Ricardo H.
TI  - A note on the approximation of free boundaries by finite element methods
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1986
SP  - 355
EP  - 368
VL  - 20
IS  - 2
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1986__20_2_355_0/
LA  - en
ID  - M2AN_1986__20_2_355_0
ER  - 
%0 Journal Article
%A Nochetto, Ricardo H.
%T A note on the approximation of free boundaries by finite element methods
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1986
%P 355-368
%V 20
%N 2
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1986__20_2_355_0/
%G en
%F M2AN_1986__20_2_355_0
Nochetto, Ricardo H. A note on the approximation of free boundaries by finite element methods. ESAIM: Modélisation mathématique et analyse numérique, Volume 20 (1986) no. 2, pp. 355-368. http://www.numdam.org/item/M2AN_1986__20_2_355_0/

[1] D Aronson, L Caffarelli, S Kamin, How an initially stationary interface begins to move in porous medium flow, SIAM J Math Anal 14, 4 (1983), pp 639-658 | MR | Zbl

[2] C Baiocchi, Estimations d erreur dans L pour les inéquations a obstacle, Mathematical Aspects of F E M , Lectures Notes m Math 606, Springer (1977), pp 27-34 | MR | Zbl

[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 | Numdam | MR | Zbl

[4] H Brezis, Seuil de régulante pour certains problèmes unilatéraux, C R Acad Sci Paris 273 (1971), pp 35-37 | MR | Zbl

[5] H Brezis, D Kinderlehrer, The smoothness of solutions to nonlinear variational inequahties Indiana Univ Math J 23, 9 (1974), pp 831-844 | MR | Zbl

[6] F Brezzi, L Caffarelli, Convergence of the discrete free boundaries for finite element approximations, RAIRO Numer Anal 17 (1983), pp 385-395 | Numdam | MR | Zbl

[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 | MR | Zbl

[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 | MR | Zbl

[9] F Brezzi, G Sacchi, A finite element approximation of a variational inequality related to hydraulics, Calcolo 13, III (1976), pp. 257-274 | MR | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[14] L Caffarelli, N Rivière, Asymptotic behavior of free boundaries at their singular points, Ann Math 106 (1977), pp 309-317 | MR | Zbl

[15] P Ciarlet, The finite element method for elliptic problems, North-Holland (1978) | MR | Zbl

[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 | Zbl

[17] A Damlamian, Some results in the multiphase Stefan problem, Comm Partial Differential Equations 2, 10 (1977), pp 1017-1044 | MR | Zbl

[18] E Di Benedetto, Continuity of weak-solutions to certain singular parabolic equations Ann Mat Pura Appl IV, 130 (1982), pp 131-176 | MR | Zbl

A boundary modulus of continuity for a class of singular parabolic equations (to appear) | Zbl

[19] A Friedman, , The Stefan problem in several space variables, Trans Amer Math Soc 133 (1968), pp 51-87 | MR | Zbl

[20] A Friedman, Variational Principles and Free-Boundary Problems, John Wiley & Sons (1982) | MR | Zbl

[21] L Jerome, M Rose, Error estimetes for the multidimensional two-phase Stefan problem, Math Comp 39, 160 (1982), pp 377-414 | MR | Zbl

[22] B Knerr, The porous medium equation in one dimension, Trans Amer Math Soc 234 (1977), pp 381-415 | MR | Zbl

[23] M Niezgodka, I Pawlow, A generalized Stefan problem in several space variables Appl Math Optim 9 (1983), pp 193-224 | MR | Zbl

[24] J Nitsche, L -convergence of finite element approximations, Mathematical Aspects of F E M, Lectures Notes m Math 606, Springer (1977), pp 261-274 | MR | Zbl

[25] 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 | Zbl

[26] 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 | Zbl

[27] 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 | Zbl

[28] 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

[29] R Rannacher, R Scott, Some optimal error estimates for piecewise linear finite element approximations Math Comp 38, 158 (1982), pp 437-445 | MR | Zbl

[30] M Rose, Numerical methods for flows through porous media I, Math Comp 40, 162 (1983), pp 435-467 | MR | Zbl

[31] 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 | Zbl