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Convergence of the ghost fluid method for elliptic equations with interfaces
Author(s):
Xu-Dong
Liu;
Thomas
C.
Sideris.
Journal:
Math. Comp.
72
(2003),
1731-1746.
MSC (2000):
Primary 65N12, 35J25
Posted:
May 14, 2003
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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:
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
Posted:
May 14, 2003
Additional Notes:
Research partially supported by the National Science Foundation: DMS-9805546 (X.-D.L.) and DMS-9800888 (T.C.S.)
Copyright of article:
Copyright
2003,
American Mathematical Society
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