A Multigrid Algorithm for Elliptic Problems Loyce Adams A second order accurate strategy, called the Immersed Interface Method was proposed by Randall LeVeque and Zhilin Li for solving elliptic problems that have possible jumps in the forcing function, the solution, the flux, or the coefficients across some internal interface that is not necessarily aligned with the computational grid. In this paper, we describe a FMG (full multigrid) strategy that works well with the immersed interface approach. Results for a variety of model problems are given.