# On the accuracy of finite element approximations to a class of interface problems

@article{Guzmn2016OnTA,
title={On the accuracy of finite element approximations to a class of interface problems},
author={Johnny Guzm{\'a}n and Manuel A. S{\'a}nchez and Marcus Sarkis},
journal={Math. Comput.},
year={2016},
volume={85},
pages={2071-2098}
}
• Published 10 November 2015
• Mathematics
• Math. Comput.
The jump is defined as [∇u · n] = ∇u · n + ∇u ·n where u = u|Ω± and n is the unit outward pointing normal to Ω (see figure 1). Also, we denote [u] = u − u. Many numerical methods have been developed for problem (1.1). Perhaps the most notable ones are the finite difference method of Peskin  (i.e., immersed boundary method) and the method of LeVeque and Li  (i.e., the immersed interface method ; see also the method of Mayo [14, 15, 16]) .The method of LeVeque and Li  was developed…

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