Abstract

We compare the Immersed Interface Method (IIM) with the Extended Finite Element Method (X-FEM) for elliptic equations with singular sources and discontinuous coeficients. 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.

Keywords

cartesian grids, discontinuous coefficient, elliptic equation, extended finite element method, finite difference methods, finite element methods, immersed interface method, immersed boundary method, irregular domain, level set methods, singular source term

Mathematical Subject Classification

Primary: 65N06, 65N30, 65N50

Authors