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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Convergence of the ghost fluid method for elliptic equations with interfaces


Authors: Xu-Dong Liu and Thomas C. Sideris
Journal: Math. Comp. 72 (2003), 1731-1746
MSC (2000): Primary 65N12, 35J25
Published electronically: May 14, 2003
MathSciNet review: 1986802
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Abstract: This paper proves the convergence of the ghost fluid method for second order elliptic partial differential equations with interfacial jumps. A weak formulation of the problem is first presented, which then yields the existence and uniqueness of a solution to the problem by classical methods. It is shown that the application of the ghost fluid method by Fedkiw, Kang, and Liu to this problem can be obtained in a natural way through discretization of the weak formulation. An abstract framework is given for proving the convergence of finite difference methods derived from a weak problem, and as a consequence, the ghost fluid method is proved to be convergent.


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Additional Information

Xu-Dong Liu
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: xliu@math.ucsb.edu

Thomas C. Sideris
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: sideris@math.ucsb.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-03-01525-4
PII: S 0025-5718(03)01525-4
Received by editor(s): August 21, 2001
Received by editor(s) in revised form: May 3, 2002
Published electronically: May 14, 2003
Additional Notes: Research partially supported by the National Science Foundation: DMS-9805546 (X.-D.L.) and DMS-9800888 (T.C.S.)
Article copyright: © Copyright 2003 American Mathematical Society