419 IGPM419.pdf        March 2015
TITLE Analysis of Highly Accurate Finite Element Based Algorithms For Computing Distances To Level Sets
AUTHORS Jörg Grande
ABSTRACT 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