Vol. 1, No. 1, 2006

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources

Benjamin Leroy Vaughan, Jr., Bryan Gerard Smith and David L. Chopp

Vol. 1 (2006), No. 1, 207–228
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.

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 2000
Primary: 65N06, 65N30, 65N50
Milestones
Received: 4 January 2006
Revised: 1 October 2006
Published: 9 May 2007
Authors
Benjamin Leroy Vaughan, Jr.
Engineering Sciences and Applied Mathematics Dept.
Northwestern University
2145 Sheridan Road
Evanston, Illinois 60208
United States
Bryan Gerard Smith
Engineering Sciences and Applied Mathematics Dept.
Northwestern University
2145 Sheridan Road
Evanston, Illinois 60208
United States
David L. Chopp
Engineering Sciences and Applied Mathematics Dept.
Northwestern University
2145 Sheridan Road
Evanston, Illinois 60208
United States