Acceso abierto

Stability of the Semi-Implicit Discrete Duality Finite Volume Scheme for the Curvature Driven Level Set Equation in 2D


Cite

[1] ANDREIANOV, B.-BOYER,F.-HUBERT, F.: Discrete duality finite volume schemes for Leray-Lions type elliptic problems on general 2D meshes, Numer. Methods Partial Differential Equations 23 (2007), 145-195.10.1002/num.20170Search in Google Scholar

[2] ALVAREZ, L.-GUICHARD, F.-LIONS, P. L.-MOREL, J. M.: Axioms and fundamental equations of image processing, Arch. Ration. Mech. Anal. 123 (1993), 200-257.10.1007/BF00375127Search in Google Scholar

[3] ANGENENT, S. B.-GURTIN, M. E.: Multiphase thermomechanics with an interfacial structure 2. Evolution of an isothermal interface, Arch. Ration. Mech. Anal. 108 (1989), 323-391.10.1007/BF01041068Search in Google Scholar

[4] CASELLES, V.-KIMMEL, R.-SAPIRO, G.: Geodesic active contours, Int. J. Comput. Vis. 22 (1997), 61-79.10.1023/A:1007979827043Search in Google Scholar

[5] CRANDALL, M. G.-ISHII, H.-LIONS, P. L.: User’s guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (NS) 27 (1992), 1-67.10.1090/S0273-0979-1992-00266-5Search in Google Scholar

[6] DECKELNICK, K.-DZIUK, G.: Error estimates for a semi-implicit fully discrete finite element scheme for the mean curvature flow of graphs, Interfaces Free Bound. 2 (2000), 341-359.10.4171/IFB/24Search in Google Scholar

[7] EVANS, L. C.-SPRUCK, J.: Motion of level sets by mean curvature I, J. Differential Geom. 33 (1991), 635-681.10.4310/jdg/1214446559Search in Google Scholar

[8] EYMARD, R.-GALLOU¨ ET, T.-HERBIN, R.: The finite volume method, in: Handbook of Numerical Analysis, Vol. 7 (Ph. Ciarlet et al., eds.), pp. 715-1022, North-Holland/ Elsevier, Amsterdam, 2000, pp. 715-1022.Search in Google Scholar

[9] HANDLOVIČOVÁ, A.-MIKULA, K.: Convergenca of the semi-implicit co-volume scheme for the curvature driven level set equation (to appear).Search in Google Scholar

[10] HANDLOVIČOVÁ,A.-MIKULA, K.-SARTI, A.: Numerical solution of parabolic equations related to level set formulation of mean curvature flow, Comput. Vis. Sci. 1 (1998), 179-182.10.1007/s007910050016Search in Google Scholar

[11] HANDLOVIČOVÁ, A.-MIKULA, K.-SGALLARI, F.: Variational numerical methods for solving nonlinear diffusion equations arising in image processing, J. Visual Communication and Image Representation 13 (2002), 217-237.10.1006/jvci.2001.0479Search in Google Scholar

[12] KICHENASSAMY, S.-KUMAR, A.-OLVER, P.-TANNENBAUM, A.-YEZZI, A.: Conformal curvature flows: from phase transitions to active vision, Arch. Ration. Mech. Anal. 134 (1996), 275-301.10.1007/BF00379537Search in Google Scholar

[13] KOTOROVÁ, D.: Discrete duality finite volume scheme for the curvature-driven level set equation, Acta Polytech. Hungarica 8 (2011), 7-12Search in Google Scholar

[14] MIKULA, K.-RAMAROSY, N.: Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing, Numer. Math. 89 (2001), 561-590.10.1007/PL00005479Search in Google Scholar

[15] OBERMAN, A. M.: A convergent monotone difference scheme for motion of level sets by mean curvature, Numer. Math. 99 (2004), 365-379.10.1007/s00211-004-0566-1Search in Google Scholar

[16] OSHER, S.-FEDKIW, R.: Level Set Methods and Dynamic Implicit Surfaces, in: Appl. Math. Sci., Vol. 153, Springer-Verlag, New York, 2003.10.1007/b98879Search in Google Scholar

[17] SARTI, A.-MALLADI, R.-SETHIAN, J. A.: Subjective surfaces: A method for completing missing boundaries, Proc. Natl. Acad. Sci. USA 97 (2000), 6258-6263.10.1073/pnas.1101357971858910823902Search in Google Scholar

[18] SETHIAN, J. A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, in: Cambridge Monogr. Appl. Comput. Math., Vol. 3, Cambridge University Press, New York, 1999 Search in Google Scholar

eISSN:
1210-3195
Idioma:
Inglés
Calendario de la edición:
3 veces al año
Temas de la revista:
Mathematics, General Mathematics