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 - <p style="text-align: justify;">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.</p>