Stability of Semi-Implicit Finite Volume Scheme for Level Set Like Equation (Communications in Mathematical Research, 2021)
We study numerical methods for level set like equations arising in image processing and curve evolution problems. Semi-implicit finite volume-elementtype schemes are constructed for the general level set like equation (image selectivesmoothing model) given by Alvarez et al. (Alvarez L, Lions P L, Morel J M. Imageselective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer.Anal., 1992, 29: 845–866). Through the reasonable semi-implicit discretization intime 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.
Keywords: level set like equation; semi-implicit; finite volume scheme; stability.