Dziuk's surface finite element method for mean curvature flow has had significant impact on the development of parametric and evolving surface finite element methods for surface evolution equations and curvature flows. However, Dziuk's surface finite element method for mean curvature flow of closed surfaces remains still open since it was proposed in 1990. In this article, we prove convergence of Dziuk's semidiscrete surface finite element method with high-order finite elements for mean curvature flow of closed surfaces by utilizing the matrix-vector formulation of evolving surface finite element methods and a monotone structure of the nonlinear discrete surface Laplacian proved in this paper.

翻译：Dziuk的表面限制元素平均曲线流方法对地表进化方程式和曲线流的参数和不断演变的表面限制元素方法产生了重大影响,但自1990年提出以来,Dziuk用于封闭表面平均曲线流的表面限制元素方法仍然开放。