An Error Estimate for a New Scheme for Mean Curvature Motion
نویسنده
چکیده
In this work, we propose a new numerical scheme for the anisotropic mean curvature equation. The solution of the scheme is not unique, but for all numerical solutions, we provide an error estimate between the continuous solution and the numerical approximation. Our scheme is also applicable to compute the solution to dislocations dynamics equation. We also provide some numerical simulations. AMS Classification: 65M06, 65M12, 65M15, 49L25, 53C44.
منابع مشابه
An Improved Motion Vector Estimation Approach for Video Error Concealment Based on the Video Scene Analysis
In order to enhance the accuracy of the motion vector (MV) estimation and also reduce the error propagation issue during the estimation, in this paper, a new adaptive error concealment (EC) approach is proposed based on the information extracted from the video scene. In this regard, the motion information of the video scene around the degraded MB is first analyzed to estimate the motion type of...
متن کاملTitle of Dissertation: Error Control for the Mean Curvature Flow Error Control for the Mean Curvature Flow
Title of Dissertation: ERROR CONTROL FOR THE MEAN CURVATURE FLOW Omar Lakkis, Doctor of Philosophy, 2002 Dissertation directed by: Professor Ricardo H. Nochetto Department of Mathematics We study the equation describing the motion of a nonparametric surface according to its mean curvature flow. This is a nonuniformly parabolic equation that can be discretized in space via a finite element metho...
متن کاملIntegration Scheme for SINS/GPS System Based on Vertical Channel Decomposition and In-Motion Alignment
Accurate alignment and vertical channel instability play an important role in the strap-down inertial navigation system (SINS), especially in the case that precise navigation has to be achieved over long periods of time. Due to poor initialization as well as the cumulative errors of low-cost inertial measurement units (IMUs), initial alignment is not sufficient to achieve required navigation ac...
متن کاملRemarks on the accuracy of algorithms for motion by mean curvature in bounded domains
Simulations of motion by mean curvature in bounded domains, with applications to bubble motion and grain growth, rely upon boundary conditions that are only approximately compatible with the equation of motion. Three closed form solutions for the problem exist, governing translation, rotation and expansion of a single interface [1], providing the only benchmarks for algorithm verification. We d...
متن کاملA Morphological Scheme for Mean Curvature Motion and Applications to Anisotropic Diffusion and Motion of Level Sets
This paper introduces a discrete scheme for mean curvature motion using a morphological image processing approach. After brieey presenting an axiomatic approach of image processing and the mean curvature PDE, the properties of the proposed scheme are studied, in particular consistency and convergence are proved. The applications of mean curvature motion in image denoising and form evolution are...
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:
- SIAM J. Numerical Analysis
دوره 46 شماره
صفحات -
تاریخ انتشار 2008