Calculus on Surfaces with General Closest Point Functions

@article{Mrz2012CalculusOS,
  title={Calculus on Surfaces with General Closest Point Functions},
  author={Thomas M{\"a}rz and Colin B. Macdonald},
  journal={SIAM J. Numerical Analysis},
  year={2012},
  volume={50},
  pages={3303-3328}
}
The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 19 references

First Order Quasi-Linear PDEs with BV Boundary Data and Applications to Image Inpainting

  • T.A.J.A. MÄRZ
  • Logos Verlag, Berlin
  • 2010
Highly Influential
3 Excerpts

Level set approach to mean curvature motion in arbitrary codimension

  • L. AMBROSIO, H. M. SONER
  • J. Diff. Geo., 43
  • 1996
Highly Influential
5 Excerpts

Differential Topology

  • M. W. HIRSCH
  • Springer Verlag
  • 1976
Highly Influential
3 Excerpts

An h-narrow band finite element method for elliptic equations on implicit surfaces

  • K. DECKELNICK, G. DZIUK, C. M. ELLIOTT, C.-J. HEINE
  • IMA J. Num. Ana., 30
  • 2010
2 Excerpts

Differential Geometry and Its Applications

  • J. OPREA
  • The Mathematical Association of America, second…
  • 2007
2 Excerpts

Similar Papers

Loading similar papers…