A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources

Abstract

We compare the Immersed Interface Method (IIM) with the Extended Finite Element Method (X-FEM) for elliptic equations with singular sources and discontinuous coefficients. The IIM has been compared favorably with a number of other competing methods. These methods are of particular interest because they allow for the solution of elliptic equations with internal boundaries on nonconforming meshes. In the context of moving interface problems, the emphasis in this paper is placed on accuracy of solutions and their normal derivatives on the interface. These methods are briefly described and the results for benchmark problems are compared.