Biomedical Engineering Reference
In-Depth Information
[12] Crandall, M. G., Ishii, H., and Lions, P. L., User's guide to viscosity so-
lutions of second order partial differential equations, Bull. (NS) Amer.
Math. Soc., Vol. 27, pp. 1-67, 1992.
[13] Deckelnick, K. and Dziuk, G., Convergence of a finite element method
for non-parametric mean curvature flow, Numer. Math., Vol. 72, pp. 197-
222, 1995.
[14] Deckelnick, K. and Dziuk, G., Error estimates for a semi implicit fully
discrete finite element scheme for the mean curvature flow of graphs,
Interfaces Free Bound., Vol. 2, No. 4, pp. 341-359, 2000.
[15] Deckelnick, K. and Dziuk, G., A fully discrete numerical scheme for
weighted mean curvature flow, Numer. Math., Vol. 91, pp. 423-452,
2002.
[16] Dziuk, G., Algorithm for evolutionary surfaces, Numer. Math., Vol. 58,
pp. 603-611, 1991.
[17] Dziuk, G., Convergence of a semi discrete scheme for the curve short-
ening flow, Math. Models Methods Appl. Sci., Vol. 4, pp. 589-606, 1994.
[18] Dziuk, G., Discrete anisotropic curve shortening flow, SIAM J. Numer.
Anal., Vol. 36, pp. 1808-1830, 1999.
[19] Evans, L. C. and Spruck, J., Motion of level sets by mean curvature I,
J. Diff. Geom., Vol. 33, pp. 635-681, 1991.
[20] Eymard, R., Gallouet, T., and Herbin, R., The finite volume method, In:
Handbook for Numerical Analysis, Vol. 7, Ciarlet, Ph., and Lions, J. L.,
eds, Elsevier, Amsterdam, 2000.
[21] Frolkovi c, P. and Mikula, K., Flux-based level set method: A finite vol-
ume method for evolving interfaces, Preprint IWR/SFB 2003-15, Inter-
disciplinary Center for Scientific Computing, University of Heidelberg,
2003.
[22] Gage, M. and Hamilton, R. S., The heat equation shrinking convex plane
curves, J. Diff. Geom., Vol. 23, pp. 69-96, 1986.
[23] Grayson, M., The heat equation shrinks embedded plane curves to round
points, J. Diff. Geom., Vol. 26, pp. 285-314, 1987.
