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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 |
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Vol. 1 (2006), No. 1, 207–228
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Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 65N06, 65N30, 65N50
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Milestones
Received: 4 January 2006
Revised: 1 October 2006
Published: 9 May 2007
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Authors |
| Benjamin Leroy Vaughan, Jr. | |
| Engineering Sciences and Applied
Mathematics Dept. Northwestern University 2145 Sheridan Road Evanston, Illinois 60208 United States |
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| Bryan Gerard Smith | |
| Engineering Sciences and Applied
Mathematics Dept. Northwestern University 2145 Sheridan Road Evanston, Illinois 60208 United States |
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| David L. Chopp | |
| Engineering Sciences and Applied
Mathematics Dept. Northwestern University 2145 Sheridan Road Evanston, Illinois 60208 United States |
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