Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2009
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| _version_ | 1866912512032636928 |
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| author | Caloz, Gabriel Dauge, Monique Péron, Victor |
| author_facet | Caloz, Gabriel Dauge, Monique Péron, Victor |
| contents | In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work, the interface between the two subdomains is supposed to be Lipschitz. We first study a scalar transmission problem which is handled through a converging asymptotic series. Then we derive uniform a priori estimates for Maxwell transmission problem set on a domain made up of a dielectric and a highly conducting material. The technique is based on an appropriate decomposition of the electric field, whose gradient part is estimated thanks to the first part. As an application, we develop an argument for the convergence of an asymptotic expansion as the conductivity tends to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0910_1018 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism Caloz, Gabriel Dauge, Monique Péron, Victor Numerical Analysis In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work, the interface between the two subdomains is supposed to be Lipschitz. We first study a scalar transmission problem which is handled through a converging asymptotic series. Then we derive uniform a priori estimates for Maxwell transmission problem set on a domain made up of a dielectric and a highly conducting material. The technique is based on an appropriate decomposition of the electric field, whose gradient part is estimated thanks to the first part. As an application, we develop an argument for the convergence of an asymptotic expansion as the conductivity tends to infinity. |
| title | Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/0910.1018 |