A note on immersed interface method for three-dimensional elliptic equations

The Immersed Interface Method proposed by LeVeque and Li [1] is extended to three-dimensional elliptic equations of the form: •(β(x) u(x))+κ(x)u(x)=f(x). We study the situation in which there is an irregular interface (surface) S contained in the solution domain across which β, κ and f may be discontinuous or even singular. As a result, the solution u will usually be nonsmooth or even discontinuous. A finite difference approach with a uniform Cartesian grid is used in the discretization. Local truncation error analysis is performed to estimate the accuracy of the numerical solution.