Convergence of Finite Difference Methods for Poisson's Equation with Interfaces

Details Convergence of Finite Difference Methods for Poisson's Equation with Interfaces Convergence of Finite Difference Methods for Poisson's Equation with Interfaces

2001-08-17

arxiv.org/abs/math/0108122v1

Mathematics

Numerical Analysis

17 pages, 3 figures

Scientific paper

In this paper, a weak formulation of the discontinuous variable coefficient Poisson equation with interfacial jumps is studied. The existence, uniqueness and regularity of solutions of this problem are obtained. 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 proven to be convergent.

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