The Immersed Interface Method for Elliptic and Parabolic Problems with Discontinuous Coefficients

@inproceedings{Aljahdaly2014TheII,
  title={The Immersed Interface Method for Elliptic and Parabolic Problems with Discontinuous Coefficients},
  author={Noufe H. Aljahdaly},
  year={2014}
}
In this paper we consider numerical methods for solving elliptic as well as time dependent advection- diffusion-reaction (ADR) equations in one spatial dimension. We consider the case in which the difference diffusion coefficients as well as advection coefficients and reaction coefficients are discontinuous across a fixed interface. Using the immersed interface method (IIM) for finite difference approximations, we demonstrate how to modify numerical methods constructed for the constant… 
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