Quadratic Rate of Convergence for Curvature Dependent Smooth Interfaces: a Simple Proof1
نویسنده
چکیده
We consider the approximation of curvature dependent geometric front evolutions by singularly perturbed parabolic double obstacle problems with small parameter ". We give a simpliied proof of optimal interface error estimates of order O(" 2), valid in the smooth regime, which is based on constructing precise barriers, perturbing the forcing term and exploiting the maximum principle.
منابع مشابه
A TRUST-REGION SEQUENTIAL QUADRATIC PROGRAMMING WITH NEW SIMPLE FILTER AS AN EFFICIENT AND ROBUST FIRST-ORDER RELIABILITY METHOD
The real-world applications addressing the nonlinear functions of multiple variables could be implicitly assessed through structural reliability analysis. This study establishes an efficient algorithm for resolving highly nonlinear structural reliability problems. To this end, first a numerical nonlinear optimization algorithm with a new simple filter is defined to locate and estimate the most ...
متن کاملConvergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
In this paper, we study the convergent property of a well known discretized scheme of Gaussian curvature, derived from Gauss-Bonnet theorem, over triangulated surface. Suppose the triangulation is obtained from a sampling of a smooth parametric surface, we show theoretically that the discretized approximation has quadratic convergence rate for a special triangulation scenario of the surface. Nu...
متن کاملA New Trust Model for B2C E-Commerce Based on 3D User Interfaces
Lack of trust is one of the key bottle necks in e-commerce development. Nowadays many advanced technologies are trying to address the trust issues in e-commerce. One among them suggests using suitable user interfaces. This paper investigates the functionality and capabilities of 3D graphical user interfaces in regard to trust building in the customers of next generation of B2C e-commerce websit...
متن کاملConvergence Analysis of Discrete Differential Geometry Operators over Surfaces
In this paper, we study the convergence property of several discrete schemes of the surface normal. We show that the arithmetic mean, area-weighted averaging, and angle-weighted averaging schemes have quadratic convergence rate for a special triangulation scenario of the surfaces. By constructing a counterexample, we also show that it is impossible to find a discrete scheme of normals that has ...
متن کاملAngle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes
We propose a discrete approximation of the Gaussian curvature over quadrilateral meshes using a linear combination of two angle deficits. Suppose a surface mesh is obtained from a sampling of a smooth parametric surface F with gij and bij as the coefficients of the first and second fundamental forms, respectively. We show theoretically that for vertices of valence four, the considered two angle...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994