Finite element approximation of a free boundary problem arising in the theory of liquid drops ans plasma physics

 Access to full text

 Full (PDF)

1. 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 Zbl0374.65053MR488847
2. J. W. BARRETT and C. M. ELLIOTT [ 1989a] Finite element approximation of a plasma equilibrum problem IMA J Numer Anal 9, 443-464 Zbl0681.76114MR1030641
3. 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 Zbl0668.76137MR985997
4. T. B. BENJAMIN and A. COCKER [ 1984] Liquid drops suspended by soap filmsPart II Proc. Roy. Soc. Lond. A 394, 33-45 Zbl0573.76091MR763503
5. H. BERESTYCKI and H. BREZIS [ 1980] On a free boundary problem arising in plasma physics Nonlinear Analysis 4, 415-436 Zbl0437.35032MR574364
6. G. CALOZ [ 1984] A free boundary problem related to axisymmetric MHD equilibria existence and numerical approximation of solutions Report of Dept Mathematics, Lausanne 
7. G. CALOZ[ 1987] : Simulation numérique des équilibres d'un plasma dans un tokomak : modélisation et études mathématiques. Thesis 650 of Dept. Mathematics, EPF-Lausanne. 
8. G. CALOZ [ 1988] : Approximation by finite element method of the model plasma problem. Dept. of Mathematics, University of Maryland. Zbl0712.76069
9. R. CHAKRABARTI [ 1988] : Numerical solution of some free boundary problems. Ph. D. Thesis, Imperial College. 
10. P. G. CIARLET [ 1988] : Introduction to Numerical Linear Algebra and Optimisation. C.U.P., Cambridge. Zbl0672.65001MR1015713
11. 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. Zbl0251.65069MR375802
12. 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. MR822334
13. P. CORTEY-DUMONT [ 1985b] : Sur les inéquations variationnelles à opérateur non coercif. M2AN.-R.A.I.R.O., 19, 195-212. MR802593
14. P. CORTEY-DUMONT [ 1985b] : On finite element approximation in the L∞-norm of variational inequalities. Numer. Math., 47, 45-57. Zbl0574.65064MR797877
15. M. CROUZEIX and J. RAPPAZ [ 1987] : On numerical approximation in bifurcation theory. Report of the Department of Mathematics, EPF-Lausanne. Zbl0687.65057
16. N. DYN and W. E. FERGUSON [ 1983] : The numerical solution of equality-constrained quadratic programming problems. Math. Comp., 163, 165-170. Zbl0527.49030MR701631
17. R. FALK [ 1974] : Error estimates for the approximation of a class of variational inequalities.Math. Comp. 28, 963-971. Zbl0297.65061MR391502
18. A. FRIEDMAN [ 1982] : Variational Principles and Free Boundary Problems. J. Wiley, New York. Zbl0564.49002MR679313
19. V. GIRAULT and P. A. RAVIART [ 1982] : An analysis of upwind schemes for the Navier-Stokes equations SIAM. J. Numer. Anal. 19, 312-333. Zbl0487.76036MR650053
20. P. GRISVARD [ 1985] : Elliptic Problems in Nonsmooth Domains, Pilman, Boston. Zbl0695.35060MR775683
21. 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. Zbl0634.76117MR840803
22. D. KINDERLEHRER and J. SPRUCK [ 1978] : Regularity in free boundary problems. Ann. Scuola N. Sup. Pissa 5, 131-148. Zbl0409.76095MR481511
23. D. KINDERLEHRER and G. STAMPACCHIA [ 1980] : An Introduction to Variational Inequalities and Their Applications. Academic Press, New York. Zbl0457.35001MR567696
24. 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. Zbl0362.65088MR488848
25. J. RAPPAZ [ 1984] : Approximation of a nondifferentiable nonlinear problem related to MHD equuibria. Numer. Math. 45, 117-133. Zbl0527.65073MR761884
26. J. F. RODRIGUES [ 1987] : Obstacle Problems in Mathematical Physics, North Holland, Amsterdam. Zbl0606.73017MR880369
27. 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. Zbl0577.65096MR799031
28. 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. Zbl0393.65026MR533616
29. G. STRANG and G. FIX [ 1973] : An Analysis of the Finite Element Method Prentice-Hall, New Jersey. Zbl0356.65096MR443377
30. R. TEMAM [ 1975] : A nonlinear eigenvalue problem : equilibrium shape of a confined plasma. Arch. Rat. Mech. Anal. 60, 51-73. Zbl0328.35069MR412637
31. R. TEMAM [ 1977] : Remarks on a free boundary problem arising in plasma physics. Comm. in P.D.E. 2, 563-585. Zbl0355.35023MR602544
32. V. THOMEE [ 1984] : Galerkin Finite Element Methods for Parabolic Problems. Lect.Notes Math. (Springer) # 1054. Zbl0528.65052MR744045

1. J. W. Barrett, Finite element approximation of a non-Lipschitz nonlinear eigenvalue problem