Convergence of Dziuk's Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-order Finite Elements

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...

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

buckling of viscoelastic composite plates using the finite strip method

در سال های اخیر، تقاضای استفاده از تئوری خطی ویسکوالاستیسیته بیشتر شده است. با افزایش استفاده از کامپوزیت های پیشرفته در صنایع هوایی و همچنین استفاده روزافزون از مواد پلیمری، اهمیت روش های دقیق طراحی و تحلیل چنین ساختارهایی بیشتر شده است. این مواد جدید از خودشان رفتارهای مکانیکی ارائه می دهند که با تئوری های الاستیسیته و ویسکوزیته، نمی توان آن ها را توصیف کرد. این مواد، خواص ویسکوالاستیک دارند....

A finite element level set method for anisotropic mean curvature flow with space dependent weight

Fast Mean-Curvature Flow via Finite-Elements Tracking

In this paper, we present a novel approach for efficiently evolving meshes using mean-curvature flow. We use a finite-elements hierarchy that supports an efficient multigrid solver for performing the semi-implicit time-stepping. Though expensive to compute, we show that it is possible to track this hierarchy through the process of surface evolution. As a result, we provide a way to efficiently ...