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}
}
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 [18] (i.e., immersed boundary method) and the method of LeVeque and Li [11] (i.e., the immersed interface method ; see also the method of Mayo [14, 15, 16]) .The method of LeVeque and Li [11] was developed… 

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