A Nonlocal Mean Curvature Flow and Its Semi-implicit Time-Discrete Approximation
نویسندگان
چکیده
منابع مشابه
A Nonlocal Mean Curvature Flow and Its Semi-implicit Time-Discrete Approximation
We address in this paper the study of a geometric evolution, corresponding to a curvature which is non-local and singular at the origin. The curvature represents the first variation of the energy Mρ(E) defined in (1.1), proposed in a recent work [5] as a variant of the standard perimeter penalization for the denoising of nonsmooth curves. To deal with such degeneracies, we first give an abstrac...
متن کاملSemi-discrete Constant Mean Curvature Surfaces
We study semi-discrete surfaces in three dimensional euclidean space which are defined on a parameter domain consisting of one smooth and one discrete parameter. More precisely, we consider only those surfaces which are glued together from individual developable surface strips. In particular we investigate minimal surfaces and constant mean curvature (cmc) surfaces with non vanishing mean curva...
متن کاملA fully discrete numerical scheme for weighted mean curvature flow
We analyze a fully discrete numerical scheme approximating the evolution of n–dimensional graphs under anisotropic mean curvature. The highly nonlinear problem is discretized by piecewise linear finite elements in space and semi–implicitly in time. The scheme is unconditionally stable und we obtain optimal error estimates in natural norms. We also present numerical examples which confirm our th...
متن کاملImplicit time discretization of the mean curvature flow with a discontinuous forcing term
We consider an implicit time discretization for the motion of a hypersurface driven by its anisotropic mean curvature. We prove some convergence results of the scheme under very general assumptions on the forcing term, which include in particular the case of a typical path of the Brownian motion. We compare this limit with other available solutions, whenever they are defined. As a by-product of...
متن کاملMean Curvature Blowup in Mean Curvature Flow
In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M t →֒ (N, h) are characterised by the blow up of the mean curvature.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2012
ISSN: 0036-1410,1095-7154
DOI: 10.1137/120863587