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Volume 31, Issue 4
Stability of Semi-Implicit Finite Volume Scheme for Level Set Like Equation

Kwang-Il Kim & Yong-Chol Son

Commun. Math. Res., 31 (2015), pp. 351-361.

Published online: 2021-05

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  • Abstract

We study numerical methods for level set like equations arising in image processing and curve evolution problems. Semi-implicit finite volume-element type schemes are constructed for the general level set like equation (image selective smoothing model) given by Alvarez et al. (Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer. Anal., 1992, 29: 845–866). Through the reasonable semi-implicit discretization in time and co-volume method for space approximation, we give finite volume schemes, unconditionally stable in $L_∞$ and $W^{1,2} (W^{1,1})$ sense in isotropic (anisotropic) diffusion domain.

  • AMS Subject Headings

65M60

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COPYRIGHT: © Global Science Press

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@Article{CMR-31-351, author = {Kim , Kwang-Il and Son , Yong-Chol}, title = {Stability of Semi-Implicit Finite Volume Scheme for Level Set Like Equation}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {4}, pages = {351--361}, abstract = {

We study numerical methods for level set like equations arising in image processing and curve evolution problems. Semi-implicit finite volume-element type schemes are constructed for the general level set like equation (image selective smoothing model) given by Alvarez et al. (Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer. Anal., 1992, 29: 845–866). Through the reasonable semi-implicit discretization in time and co-volume method for space approximation, we give finite volume schemes, unconditionally stable in $L_∞$ and $W^{1,2} (W^{1,1})$ sense in isotropic (anisotropic) diffusion domain.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.04.07}, url = {http://global-sci.org/intro/article_detail/cmr/18919.html} }
TY - JOUR T1 - Stability of Semi-Implicit Finite Volume Scheme for Level Set Like Equation AU - Kim , Kwang-Il AU - Son , Yong-Chol JO - Communications in Mathematical Research VL - 4 SP - 351 EP - 361 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.04.07 UR - https://global-sci.org/intro/article_detail/cmr/18919.html KW - level set like equation, semi-implicit, finite volume scheme, stability. AB -

We study numerical methods for level set like equations arising in image processing and curve evolution problems. Semi-implicit finite volume-element type schemes are constructed for the general level set like equation (image selective smoothing model) given by Alvarez et al. (Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer. Anal., 1992, 29: 845–866). Through the reasonable semi-implicit discretization in time and co-volume method for space approximation, we give finite volume schemes, unconditionally stable in $L_∞$ and $W^{1,2} (W^{1,1})$ sense in isotropic (anisotropic) diffusion domain.

Kwang-Il Kim & Yong-Chol Son. (2021). Stability of Semi-Implicit Finite Volume Scheme for Level Set Like Equation. Communications in Mathematical Research . 31 (4). 351-361. doi:10.13447/j.1674-5647.2015.04.07
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