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

References

Publications referenced by this paper.
Showing 1-10 of 33 references

The inverse mean curvature flow and p-harmonic functions

R. Moser
preprint U Bath • 2005
View 9 Excerpts
Highly Influenced

Numerische Verfahren zur Berechnung von Krümmungsflüssen

E. Pasch
Ph. D. Dissertation, Universität Tübingen • 1998
View 4 Excerpts
Highly Influenced

The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality

TOM ILMANEN
1998
View 10 Excerpts
Highly Influenced

Level set methods and dynamic implicit surfaces

Applied mathematical sciences • 2003
View 1 Excerpt

Spacetime and Geometry - An Introduction to General Relativity

S. M. Carroll
Addison Wesley • 2003

Elliptic Partial Differential Equations of Second Order

D. Gilbarg, N. Trudinger
Springer-Verlag, Third Edition • 2001
View 1 Excerpt

Proof of the Riemannian Penrose Inequality using the Positive Mass Theorem

H. Bray
J. Diff. Geom., 59 • 2001

Contracting spacelike hypersurfaces by their inverse mean curvature

M. Holder
J. Austral. Math. Soc. Ser. A.68 • 2000
View 1 Excerpt

A note on the inverse mean curvature flow

G. Huisken, T. Ilmanen
Proceedings of Workshop at Saitama University • 1997
View 2 Excerpts

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