|| IGPM419.pdf March 2015 |
|| 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.
|| finite elements, level sets, quasi-distance, gradient recovery, semismooth Newton method, convergence analysis