|Preprint-No.:||< 419 >||Published in:||March 2015||PDF-File:||IGPM419.pdf|
|Title:||Analysis of Highly Accurate Finite Element Based Algorithms For Computing Distances To Level Sets|
The signed distance function d to an embedded (hyper-) surface Γ is required in the analysis and implementation of some higher order methods for the numerical treatment of partial differential equations on surfaces. Two algorithms for the approximation of d are presented in this paper, which only require a finite element approximation of a (smooth) level set function of Γ. One method is based on a semismooth Newton method; the other method is a nested fixed point iteration. Both are generalizations of known methods. We provide full (local) convergence analyses. Moreover, the methods are compared in two numerical experiments.
|Keywords:||finite elements, level sets, quasi-distance, gradient recovery, semismooth Newton method, convergence analysis|