the immersed interface method for elliptic equations with discontinuous coefficients and singular sources

@article{LeVeque1994theII,
  title={the immersed interface method for elliptic equations with discontinuous coefficients and singular sources},
  author={Randall J. LeVeque and Zhilin Li},
  journal={SIAM Journal on Numerical Analysis},
  year={1994},
  volume={31},
  pages={1019-1044}
}
The authors develop finite difference methods for elliptic equations of the form \[ \nabla \cdot (\beta (x)\nabla u(x)) + \kappa (x)u(x) = f(x)\] in a region $\Omega $ in one or two space dimension... 

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