Convergence of Finite Difference Methods for Poisson's Equation with Interfaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2001
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| _version_ | 1866915560041742336 |
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| author | Liu, Xu-Dong Sideris, Thomas C. |
| author_facet | Liu, Xu-Dong Sideris, Thomas C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0108122 |
| institution | arXiv |
| publishDate | 2001 |
| record_format | arxiv |
| spellingShingle | Convergence of Finite Difference Methods for Poisson's Equation with Interfaces Liu, Xu-Dong Sideris, Thomas C. Numerical Analysis Analysis of PDEs 65N12; 35J25 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. |
| title | Convergence of Finite Difference Methods for Poisson's Equation with Interfaces |
| topic | Numerical Analysis Analysis of PDEs 65N12; 35J25 |
| url | https://arxiv.org/abs/math/0108122 |