419	RWTH Publication No: 464321        2015        IGPM419.pdf
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
DOI	10.1137/15M1011524
PUBLICATION	SIAM Journal on Numerical AnalysisVol. 55, Iss. 1 (2017)