Open Access

Convergence of the Numerical Scheme for Regularised Riemannian Mean Curvature Flow Equation


Cite

[1] EYMARD, R.—HANDLOVIČOVÁ, A.—MIKULA, K.: Study of a finite volume scheme for regularised mean curvature flow level set equation, IMA J. Numer. Anal. 31 (2011), 813–846.10.1093/imanum/drq025Search in Google Scholar

[2] OSHER, S.—SETHIAN, J. A.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79 (1988), 12–49.10.1016/0021-9991(88)90002-2Open DOISearch in Google Scholar

[3] MIKULA, K.—SARTI, A.—SGALLARRI, A.: Co-volume method for Riemannian mean curvature flow in subjective surfaces multiscale segmentation, Comput. Vis. Sci. 9 (2006), 23–31.10.1007/s00791-006-0014-0Open DOISearch in Google Scholar

[4] ______ Co-volume level set method in subjective surface based medical image segmentation, in: Handbook of Medical Image Analysis: Segmentation and Registration Models (J. Suri et al., eds.), Springer, New York, 2005, pp. 583–626.Search in Google Scholar

[5] 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

[6] TIBENSKÝ, M.: Využitie Metód Založených na Level Set Rovnici v Spracovaní Obrazu. Faculty of mathematics, physics and informatics, Comenius University, Bratislava, 2016.Search in Google Scholar

[7] DRONIOU, J.—NATARAJ, N.: Improved L2estimate for gradient schemes and super- convergence of the TPFA finite volume scheme, IMA J. Numer. Anal. 38 (2018), 1254–1293.10.1093/imanum/drx028Open DOISearch in Google Scholar

[8] EYMARD, R.—GALLOUET, T.—HERBIN, R.: Finite volume approximation of elliptic problems and convergence of an approximate gradient, Appl. Numer. Math. 37 (2001), 31–53.10.1016/S0168-9274(00)00024-6Search in Google Scholar

[9] ______ Discretisation of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces, IMA J. Numer. Anal. 30 (2010), 1009–1043.10.1093/imanum/drn084Open DOISearch in Google Scholar

eISSN:
1210-3195
Language:
English
Publication timeframe:
3 times per year
Journal Subjects:
Mathematics, General Mathematics