Gradient-flow techniques for the analysis of numerical schemes for multi-phase mean-curvature flow
نویسندگان
چکیده
منابع مشابه
Local Techniques for Mean Curvature Flow
of ann-dimensional manifold without boundary into Euclidean space. We say Af = x(Mn) moves by mean curvature if there exists a one-parameter family Xt = x( ·, t) of immersions with corresponding images J..!I1 = x 1(lvfn) satisfying d dtx(p,t) = -H(p,t)v(p,t) (1) x(p,O) = xo(P) for some initial data xo. Here H(p,t) and v(p,t) denote mean curvature and outer unit normal of the hypersurface M 1 at...
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 کاملPhase field method for mean curvature flow with boundary constraints
This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the AllenCahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn...
متن کاملThe Mean Curvature Flow for Isoparametric Submanifolds
A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean space and sphere. We show that the mean curvature flow preserves the isoparametric condition, develops singularities in finite time, and converges in finite ...
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: Geometric Flows
سال: 2018
ISSN: 2353-3382
DOI: 10.1515/geofl-2018-0006