A convergent finite element algorithm for generalized mean curvature flows of closed surfaces

نویسندگان

چکیده

Abstract An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse and powers flow. Error estimates are proved semidiscretizations full discretizations the The studied here combines evolving surface finite elements, whose nodes determine discrete surface, linearly implicit backward difference formulae time integration. numerical method based on a system coupling evolution to nonlinear second-order parabolic equations normal velocity vector. A convergence proof presented in case elements polynomial degree at least 2 orders 5. error analysis stability consistency yield optimal-order $H^1$-norm bounds computed position, velocity, vector, therefore curvature. performed matrix–vector formulation independent geometric arguments, only enter analysis. Numerical experiments illustrate results also report monotone quantities, e.g. Hawking mass flow, complemented by nonconvex surfaces.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Finite element approximations to surfaces of prescribed variable mean curvature

We give an algorithm for finding finite element approximations to surfaces of prescribed variable mean curvature, which span a given boundary curve. We work in the parametric setting and prove optimal estimates in the H 1 norm. The estimates are verified computationally. Mathematics Subject Classification (1991): 65N30 · 49Q05 · 53A10

متن کامل

Generalized inverse mean curvature flows in spacetime

Motivated by the conjectured Penrose inequality and by the work of Hawking, Geroch, Huisken and Ilmanen in the null and the Riemannian case, we examine necessary conditions on flows of two-surfaces in spacetime under which the Hawking quasilocal mass is monotone. We focus on a subclass of such flows which we call uniformly expanding, which can be considered for null as well as for spacelike dir...

متن کامل

Finite Element Approximations and the Dirichlet Problem for Surfaces of Prescribed Mean Curvature

We give a nite element procedure for the Dirichlet Problem corresponding to surfaces of prescribed mean curvature and prove an optimal convergence estimate in the H 1-norm. 1. H-Harmonic Maps The numerical solution of the classical H-Plateau Problem consists of approximating disc-like surfaces with prescribed boundary curve and prescribed mean curvature H. For a detailed discussion of the algor...

متن کامل

Aleksandrov’s Theorem: Closed Surfaces with Constant Mean Curvature

We present Aleksandrov’s proof that the only connected, closed, ndimensional C hypersurfaces (in R) of constant mean curvature are the spheres.

متن کامل

Numerical computation of constant mean curvature surfaces using finite elements

This paper presents a method for computing two-dimensional constant mean curvature surfaces. The method in question uses the variational aspect of the problem to implement an efficient algorithm. In principle it is a flow like method in that it is linked to the gradient flow for the area functional, which gives reliable convergence properties. In the background a preconditioned conjugate gradie...

متن کامل

ذخیره 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: Ima Journal of Numerical Analysis

سال: 2021

ISSN: ['1464-3642', '0272-4979']

DOI: https://doi.org/10.1093/imanum/drab043