Discrete anisotropic curvature flow of graphs
Deckelnick, Klaus ; Dziuk, Gerhard
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 33 (1999), p. 1203-1222 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{M2AN_1999__33_6_1203_0,
     author = {Deckelnick, Klaus and Dziuk, Gerhard},
     title = {Discrete anisotropic curvature flow of graphs},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {33},
     year = {1999},
     pages = {1203-1222},
     mrnumber = {1736896},
     zbl = {0948.65138},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1999__33_6_1203_0}
}

Deckelnick, Klaus; Dziuk, Gerhard. Discrete anisotropic curvature flow of graphs. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 33 (1999) pp. 1203-1222. http://gdmltest.u-ga.fr/item/M2AN_1999__33_6_1203_0/

[1] S. B. Angenent and M. E. Gurtin, Multiphase thermomechanics with interfacial structure 2, evolution of an isothermal interface Arch. Rational Mech. Anal. 108 (1989) 323-391. | MR 1013461 | Zbl 0723.73017

[2] G. Bellettini and M. Paolini, Anisotropic motion by mean curvature in the context of Finsler geometry Hokkaido Math. J. 25 (1996) 537-566. | MR 1416006 | Zbl 0873.53011

[3] P. Clément, Approximation by finite element functions using local regularization RAIRO Anal. Numér. 9 (1975) 77-84. | Numdam | MR 400739 | Zbl 0368.65008

[4] K. Deckelnick and G. Dziuk, Convergence of a finite element method for non-parametric mean curvature flow. Numer. Math. 72 (1995) 197-222. | MR 1362260 | Zbl 0838.65103

[5] M. Dobrowolski, L∞-convergence of linear finite element approximation to nonlinear parabolic problems. SIAM J. Numer. Anal. 17 (1980) 663-674. | MR 588752 | Zbl 0449.65077

[6] Y. Giga, Motion of a graph by convexified energy. Hokkaido Math. J. 23 (1994) 185-212. | MR 1263830 | Zbl 0824.35051

[7] P. M. Girão and R. V. Kohn, Convergence of a crystalline algorithm for the heat equation in one dimension and for the motion of a graph by weighted curvature. Numer. Math. 67 (1994) 41-70. | MR 1258974 | Zbl 0791.65063

[8] G. Huisken, Non-parametric mean curvature evolution with boundary conditions. J. Differential Equations 77 (1989) 369-378. | MR 983300 | Zbl 0686.34013

[9] C. Johnson and V. Thomeé, Error estimates for a finite element approximation of a minimal surface. Math. Comp. 29 (1975) 343-349. | MR 400741 | Zbl 0302.65086

[10] O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'Tseva, Linear and quasilinear equations of parabolic type. Amer. Math. Soc, Providence, R. I. (1968).

[11] G. A. Lieberman, The first initial-boundary value problem for quasilinear second order parabolic equations. Ann. Scuola. Norm. Su. Pisa. Cl. Sci. Ser. IV. 8 (1986) 347-387. | Numdam | MR 881097 | Zbl 0655.35047

[12] V. I. Oliker and N. N. Uraltseva, Evolution of nonparametric surfaces with speed depending on curvature, II. The mean curvature case Preprint. | MR 1193345 | Zbl 0808.53004

[13] M. Rumpf, et al., GRAPE, Graphics Programming. Environment Report 8, SFB 256, Bonn (1990).

[14] J. E. Taylor, J. W. Cahn and C. A. Handwerker, Geometric models of crystal growth. Acta Metall. Mater. 40 1443-1474 (1992).