Abstract
The subject of this paper is the evolution of hypersurfaces Γ(t) ⊂ ℝd according to the law
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References
G. Bellettini, M. Paolini: Anisotropic motion by mean curvature in the context of Finsler geometry. Hokkaido Math. J., 25, 537–566, 1996
V. Caselles, R. Kirnmel, G. Sapiro, C. Sbert: Minimal surfaces: a geometric three dimensional segmentation approach. Numer. Math., 77, 423–451, 1997
Y.-G. Chen, Y. Giga, S. Goto: Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. Diff. Geom, 33, 749–786, 1991
U. Clarenz, G. Dziuk, M. Rumpf: On generalized mean curvature flow in surface processing. This volume.
K. Deckelnick, G. Dziuk: A fully discrete numerical scheme for weighted mean curvature flow. Numer. Math., to appear
K. Deckelnick, G. Dziuk: Convergence of a finite element method for non-parametric mean curvature flow. Numer. Math., 72, 197–222, 1995
K. Deckelnick, G. Dziuk: Discrete anisotropic curvature flow of graphs. Math. Modelling Numer. Anal., 33, 1203–1222, 1999
K. Deckelnick, G. Dziuk: Convergence of numerical schemes for the approximation of level set solutions to mean curvature flow. Preprint Mathematische Fakultät Freiburg, 00–17, 2000
K. Deckelnick, G. Dziuk: Error estimates for a semi-implicit fully discrete finite element method scheme for the mean curvature flow of graphs. Interfaces and Free Boundaries, 2, 341–359, 2000
G. Dziuk: Discrete anisotropic curve shortening flow. SIAM J. Numer. Anal., 36, 1808–1830, 1999
G. Dziuk: Numerical schemes for the mean curvature flow of graphs. In: P. e. a. Argoul (ed) IUTAM Symposium on Variations of Domains and Free-Boundary Problems in Solid Mechanics., 63–70. Kluwer Academic Publishers, 1999
L. Evans, J. Spruck: Motion of level sets by mean curvature I. J. Diff. Geom., 33, 636–681, 1991
M. Fried, A. Veeser: Simulation and numerical analysis of dendritic growth. In: B. Fiedler (ed) Ergodic theory, analysis, and efficient simulation of dynamical systems. 225–252, Springer, 2001
S. Osher, J. A. Sethian: Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comp. Phys., 79 12–49, 1988
M. Preußer, T. Rumpf: A level set method for anisotropic geometric diffusion in 3d image processing. Report SFB 256 Bonn, 37, 2000
A. Schmidt: Computation of three dimensional dendrites with finite elements. J. Comp. Phys., 125, 293–312, 1996
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Deckelnick, K., Dziuk, G. (2003). A Finite Element Level Set Method for Anisotropic Mean Curvature Flow with Space Dependent Weight. In: Hildebrandt, S., Karcher, H. (eds) Geometric Analysis and Nonlinear Partial Differential Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55627-2_15
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DOI: https://doi.org/10.1007/978-3-642-55627-2_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44051-2
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