论文标题
在较高规范中的正则级别集合流的有限元近似值的先验错误估计值
A priori error estimates for finite element approximations of regularized level set flows in higher norms
论文作者
论文摘要
本文证明了$ h^2 $符合有限元的方程式的错误估计值，这些方程式通过平均曲率的不同幂对表面的流进行建模（这包括平均曲率流）。对于最初在[17]中提出的针对反向平均曲率流的适应方案。该方案基于已知的正则化过程，并产生不同类型的错误，正则化错误，正规化问题的有限元离散误差以及完整的错误。在文献和自己的先前工作中，对上述错误类型的不同方面进行了处理，但在这里，我们仅，首次将重点放在$ w^{2，μ} $ norm中的有限元离散误差上，以分析正规化参数的依赖性。
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 $W^{2,μ}$ norm for the regularized equation analyzing also the dependencies from the regularization parameter.
