A novel higher order compact-immersed interface approach for elliptic problems

We present a new higher-order accurate finite difference explicit jump Immersed Interface Method for solving two-dimensional elliptic problems with singular source and discontinuous coefficients in the irregular region on a compact Cartesian mesh. We propose a new strategy for discretizing the solution at irregular points on a nine-point compact stencil such that the higher-order compactness is maintained throughout the whole computational...