Stability of Semi-implicit Finite Volume Scheme for Level Set Like Equation

摘要

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 W1,2(W1,1) sense in isotropic(anisotropic) diffusion domain.