Convergence of the ghost fluid method for elliptic equations with interfaces
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- by Xu-Dong Liu and Thomas C. Sideris PDF
- Math. Comp. 72 (2003), 1731-1746 Request permission
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.References
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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
- 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.)
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 72 (2003), 1731-1746
- MSC (2000): Primary 65N12, 35J25
- DOI: https://doi.org/10.1090/S0025-5718-03-01525-4
- MathSciNet review: 1986802