This paper proves error estimates for $H^2$ conforming finite elements for equations which model the flow of surfaces by different powers of the mean curvature (this includes mean curvature flow). for an adapted scheme originally proposed in [17] for the inverse mean curvature flow. The scheme is based on a known regularization procedure and produces different kinds of errors, a regularization error, a finite element discretization error for the regularized problems and a full error. While in the literature and own previous work different aspects of the aforementioned error types are treated, here, we solely and for the first time focus on the finite element discretization error in the $W^{2,\mu}$ norm for the regularized equation analyzing also the dependencies from the regularization parameter.

翻译：本文证明对以平均曲线(这包括平均曲线流)不同功率模拟表面流动的方程(包括平均曲线流)的2美元符合限定要素的误差估计值。对于最初在[17]年为反平均曲线流提出的经调整的方案,这个方案基于已知的正规化程序,产生不同种类的错误、正规化错误、规范化问题和完全错误。虽然在文献和自己的以往工作中,上述错误类型的不同方面得到了处理,但在这里,我们只和第一次侧重于对正规化方程式的值$W ⁇ 2,\mu}$规范中的有限分解错误,同时还分析了正规化参数的依存性。