On the a posteriori error analysis for equations of prescribed mean curvature

Mathematics of Computation

Volumn 72, Issue 244, 2003, Pages 1611-1634

  Fierro, Francesca ^a   Veeser, Andreas ^b  

^a UNIVERSITY OF MILAN   (Italy)

^b UNIVERSITY OF FREIBURG   (Germany)

Author keywords

A posteriori error estimates; Adaptive finite element methods; Nonparametric minimal surfaces; Prescribed mean curvature equations

Indexed keywords

EID: 0141976340     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-03-01507-2     Document Type: Article

References (20)

1. [AO00] Mark Ainsworth and J. Tinsley Oden, A posteriori error estimation in finite element analysis, John Wiley, New York, 2000.
2. [Bän91a] Eberhard Bänsch, Local mesh refinement in 2 and 3 dimensions, IMPACT Comput. Sci. Eng. 3 (1991), no. 3, 181-191. MR 92h:65150
3. [Bän91b] Eberhard Bänsch, An adaptive finite-element strategy for the three-dimensional time-dependent Navier-Stokes equations, J. Comp. Appl. Math, 36 (1991), no: 1, 3-28. MR 92f:76066
4. [BR78a] Ivo Babuška and Werner .C, Rheinboldt, A-posteriori error estimates for the finite element method, Internat. J. Numer. Methods Engrg. 12 (1978), 1597-1615.
5. [BR78b] Ivo Babuška and Werner C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 (1978), 736-754. MR 58:3400
6. [Cia78] Philippe G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications, vol. 4, North-Holland, Amsterdam, 1978, MR 58:25001
7. [Cia88] Philippe G. Ciarlet, Introduction to numerical linear algebra and optimization, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge etc., 1989. MR 90k:65001
8. [DHKW92] Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, and Ortwin Wohlrab, Minimal surfaces I. Boundary value problems, Grundlehren der mathematischen Wissenschaften, vol. 295, Springer-Verlag Berlin Heidelberg, 1992. MR 94c:49001a
9. [Dör96] Willy Dörfler, A convergent adaptive algorithm for Poisson's equation, SIAM J. Numer. Anal. 33 (1996), 1106-1124. MR 97e:65139
10. [DR98] Willy Dörfler and Martin Rumpf, An adaptive strategy for elliptic problems including a posteriori controlled boundary approximation, Math. Comp. 67 (1998), no. 224, 1361-1382. MR 99b:65141
11. [Fie98] Francesca Fierro, Numerical approximation of the mean curvature flow with nucleation using implicit time-stepping: an adaptive algorithm, Calcolo 35 (1998), 205-224. MR 2001e:65120
12. [Gia74] , Mariano Giaquinta, On the Dirichlet problem for surfaces of prescribed mean curvature, Manuscripta Math. 12 (1974), 73-86. MR 49:1306
13. [GT83] David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, second ed., Springer, New York, 1983. MR 86c:35035
14. [Hac92] Wolfgang Hackbusch, Elliptic differential equations. Theory and numerical treatment, Springer Series in Computational Mathematics, vol. 18, Springer, New York, 1992. MR 94b:35001
15. [MNS] Pedro Morin, Ricardo H. Nochetto, and Kunibert G. Siebert, Local problems on stars: a posteriori error estimators, convergence, and performance, Math. Comp., posted on November 7, 2002, PII S0025-5718(02)-01463-1 (to appear in print).
16. [MNS00] Pedro Morin, Ricardo H. Nochetto, and Kunibert G. Siebert, Data oscillation and convergence of adaptive FEM, SIAM J. Numer. Anal. 38 (2000), no. 2, 466-488. MR 2001g:65157
17. [Ser69] James Serrin, The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables, Philos. Trans. Roy. Soc. London Ser. A 264 (1969), 413-496. MR 43:7772
18. [SZ90] L. Ridgway Scott and Shangyou Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp. 54 (1990), no. 190, 483-493. MR 90j:65021
19. [Ver94] Rüdiger Verfürth, A posteriori error estimates for nonlinear problems. Finite element discretizations, of elliptic equations, Math. Comp. 62 (1994), no. 206, 445-475. MR 94j:65136
20. [Ver96] Rüdiger Verfürth, A review of a posteriori error estimation and adaptive meshrefinement techniques, Advances in Numerical Mathematics, John Wiley, Chichester, 1996.