Error analysis of finite element approximations of the inverse mean curvature flow arising from the general relativity

@article{Feng2007ErrorAO,
title={Error analysis of finite element approximations of the inverse mean curvature flow arising from the general relativity},
author={Xiaobing Feng and Michael Neilan and Andreas Prohl},
journal={Numerische Mathematik},
year={2007},
volume={108},
pages={93-119}
}

This paper proposes and analyzes a finite element method for a nonlinear singular elliptic equation arising from the black hole theory in the general relativity. The nonlinear equation, which was derived and analyzed by Huisken and Ilmanen in [16], represents a level set formulation for the inverse mean curvature flow describing the evolution of a hypersurface whose normal velocity equals the reciprocal of its mean curvature. We first propose a finite element method for a regularized flow which… CONTINUE READING