A priori error estimates for finite element approximations of regularized level set flows in higher norms

摘要

This paper proves error estimates for H~2 conforming finite elements for elliptic equations which model the flow of surfaces by different powers of the mean curvature (this includes 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 higher norms for the regularized equation and additionally analyze also the dependencies from the regularization parameter.