Finite element approximation of a free boundary problem arising in the theory of liquid drops ans plasma physics
ESAIM: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 2, pp. 213-252. 
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     author = {Barrett, John W. and Elliott, Charles M.},
     title = {Finite element approximation of a free boundary problem arising in the theory of liquid drops ans plasma physics},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {213--252},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {25},
     number = {2},
     year = {1991},
     mrnumber = {1097145},
     zbl = {0709.76086},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1991__25_2_213_0/}
}
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Barrett, John W.; Elliott, Charles M. Finite element approximation of a free boundary problem arising in the theory of liquid drops ans plasma physics. ESAIM: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 2, pp. 213-252. http://www.numdam.org/item/M2AN_1991__25_2_213_0/

C. Baiocchi [ 1977] Estimations d'erreur dans L∞ pour les inéquations à obstacle In Mathematical Aspects of Finite Element Methods, Rome, 1975 Springer Lecture Notes Math 606, pp 27-34 | MR | Zbl

J. W. Barrett and C. M. Elliott [ 1989a] Finite element approximation of a plasma equilibrum problem IMA J Numer Anal 9, 443-464 | MR | Zbl

J. W. Barrett and C. M. Elliott [ 1989b] Remarks concerning a free boundary problem arising in the theory of liquid drops and plasma physics Proc Roy Soc Edin A 111, 169-181 | MR | Zbl

T. B. Benjamin and A. Cocker [ 1984] Liquid drops suspended by soap filmsPart II Proc. Roy. Soc. Lond. A 394, 33-45 | MR | Zbl

H. Berestycki and H. Brezis [ 1980] On a free boundary problem arising in plasma physics Nonlinear Analysis 4, 415-436 | MR | Zbl

G. Caloz [ 1984] A free boundary problem related to axisymmetric MHD equilibria existence and numerical approximation of solutions Report of Dept Mathematics, Lausanne

G. Caloz[ 1987] : Simulation numérique des équilibres d'un plasma dans un tokomak : modélisation et études mathématiques. Thesis 650 of Dept. Mathematics, EPF-Lausanne.

G. Caloz [ 1988] : Approximation by finite element method of the model plasma problem. Dept. of Mathematics, University of Maryland.

R. Chakrabarti [ 1988] : Numerical solution of some free boundary problems. Ph. D. Thesis, Imperial College.

P. G. Ciarlet [ 1988] : Introduction to Numerical Linear Algebra and Optimisation. C.U.P., Cambridge. | MR | Zbl

P. G. Ciarlet and P. Raviart [ 1973] : Maximum principle and uniform convergence for the finite element method. Comp. Meth. Appl. Mech. Eng. 2, 17-31. | MR | Zbl

A. Cocker, A. Friedman and J. B. Mcleod [ 1986] : A variational inequality associated with liquid on a soap film. Arch. Rat. Mech. Anal. 93, 15-45. | MR

P. Cortey-Dumont [ 1985b] : Sur les inéquations variationnelles à opérateur non coercif. M2AN.-R.A.I.R.O., 19, 195-212. | Numdam | MR

P. Cortey-Dumont [ 1985b] : On finite element approximation in the L∞-norm of variational inequalities. Numer. Math., 47, 45-57. | MR | Zbl

M. Crouzeix and J. Rappaz [ 1987] : On numerical approximation in bifurcation theory. Report of the Department of Mathematics, EPF-Lausanne. | Zbl

N. Dyn and W. E. Ferguson [ 1983] : The numerical solution of equality-constrained quadratic programming problems. Math. Comp., 163, 165-170. | MR | Zbl

R. Falk [ 1974] : Error estimates for the approximation of a class of variational inequalities.Math. Comp. 28, 963-971. | MR | Zbl

A. Friedman [ 1982] : Variational Principles and Free Boundary Problems. J. Wiley, New York. | MR | Zbl

V. Girault and P. A. Raviart [ 1982] : An analysis of upwind schemes for the Navier-Stokes equations SIAM. J. Numer. Anal. 19, 312-333. | MR | Zbl

P. Grisvard [ 1985] : Elliptic Problems in Nonsmooth Domains, Pilman, Boston. | MR | Zbl

F. Klkuchl, K. Nakazota and T. Ushijima [ 1984] : Finite element approximation of a nonlinear eigenvalue problem related to MHD equilibria. Japan J. Appl. Math. 1, 369-403. | MR | Zbl

D. Kinderlehrer and J. Spruck [ 1978] : Regularity in free boundary problems. Ann. Scuola N. Sup. Pissa 5, 131-148. | Numdam | MR | Zbl

D. Kinderlehrer and G. Stampacchia [ 1980] : An Introduction to Variational Inequalities and Their Applications. Academic Press, New York. | MR | Zbl

J. A. Nitsche [ 1977]: L∞-convergence of finite element approximations. In: Mathematical Aspects of Finite Element Methods, Rome. 1975. Springer Lectures Notes Math., 606,pp. 1-15. | MR | Zbl

J. Rappaz [ 1984] : Approximation of a nondifferentiable nonlinear problem related to MHD equuibria. Numer. Math. 45, 117-133. | MR | Zbl

J. F. Rodrigues [ 1987] : Obstacle Problems in Mathematical Physics, North Holland, Amsterdam. | MR | Zbl

A. Schatz[ 1985] : An introduction to the analysis of the error in the finite element method for second-order elliptic boundary value problems. In : Numerical Analysis Lancaster 1984. Springer Lecture Notes, Math., 1129, pp. 94-139. | MR | Zbl

M. Sermange [ 1979] : Une méthode numérique en bifurcation - une application à un problème à frontière libre de la physique des plasmas. Appl. Math. Optim. 5, 127-151. | MR | Zbl

G. Strang and G. Fix [ 1973] : An Analysis of the Finite Element Method Prentice-Hall, New Jersey. | MR | Zbl

R. Temam [ 1975] : A nonlinear eigenvalue problem : equilibrium shape of a confined plasma. Arch. Rat. Mech. Anal. 60, 51-73. | MR | Zbl

R. Temam [ 1977] : Remarks on a free boundary problem arising in plasma physics. Comm. in P.D.E. 2, 563-585. | MR | Zbl

V. Thomee [ 1984] : Galerkin Finite Element Methods for Parabolic Problems. Lect.Notes Math. (Springer) # 1054. | MR | Zbl