Finite element approximations to surfaces of prescribed variable mean curvature

Numerische Mathematik

Volumn 102, Issue 4, 2006, Pages 611-648

  Dziuk, Gerhard ^a   Hutchinson, John E ^b  

^a UNIVERSITY OF FREIBURG   (Germany)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31744432035     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-005-0649-7     Document Type: Article

References (16)

1. [Be] Berger, M.: Nonlinearity and Functional Analysis. Academic Press 1977
2. [DHKW] Dierkes, U., Hildebrandt, S., Küster, A., Wohlrab, O.: Minimal Surfaces I & II. Springer 1992
3. [DH1] Dziuk, G., Hutchinson, J.E.: On the Approximation of Unstable Parametric Minimal Surfaces. Calc. Var. 4, 27-58 (1996)
4. [DH2] Dziuk, G., Hutchinson, J.E.: Finite Element Approximations and the Dirichlet Problem for Surfaces of Prescribed Mean Curvature. In: H.-C. Hege, K. Polthier (eds.), Mathematical visualization, Springer, Berlin-Heidelberg-New York, 1998, pp. 73-87
5. [DH3] Dziuk, G., Hutchinson, J.E.: The Discrete Plateau Problem: Algorithm and Numerics. Math. Comp. 68, 1-23 (1999)
6. [DH4] Dziuk, G., Hutchinson, I.E.: The Discrete Plateau Problem: Convergence Results. Math. Comp. 68, 519-546 (1999)
7. [He] Heinz, E.: Über das Randverhalten quasilinearer elliptischer Systeme mit isothermen Parametern. Math. Zeit. 113, 99-105 (1970)
8. [Hil] Hildebrandt, S.: Boundary Behaviour of Minimal Surfaces. Arch. Rat. Mech. Anal. 35, 47-82 (1969)
9. [Imb] Imbusch, C.: Eine Anwendung des Mountain-Pass-Lemmas auf den Fragenkreis des Plateauschen Problems und eine Alternative zur Drei-Punkte-Bedingung. Bonn Mathematical Publications 302, Universität Bonn, Mathematisches Institut, Bonn, 1997
10. 1,α-Rändern. Nachr. Akad. Wiss. Gött., II. Math. Phys. Kl. (1977), Nr. 5
11. [N1] Nitsche, J.C.C.: The Boundary Behaviour of Minimal Surfaces. Kellogg's Theorem and Branch Points on the Boundary. Invent. Math. 8, 313-333 (1969)
12. 2 -estimate for the discrete Plateau problem. Math. Comp. 73, 1763-1777 (2004)
13. [P2] Pozzi, P.: The discrete Douglas problem: theory and numerics. Interfaces Free Bound. 6, 219-252 (2004)
14. [P3] Pozzi, P.: The discrete Douglas problem: convergence results. IMA J. Numer. Anal. 25, 337-378 (2005)
15. [St1] Struwe, M.: Plateau's Problem and the Calculus of Variations. Mathematical Notes 35, Princeton University Press, 1988
16. [St2] Struwe, M.: Multiple solutions to the Dirichlet problem for surfaces of prescribed mean curvature. In: Analysis, et cetera, Academic Press, 1990, pp. 639-666