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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
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