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