期刊
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
卷 19, 期 -, 页码 635-660出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0956792508007729
关键词
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资金
- MiUR [2006014115]
- GNAMPA
We deal with a variational approach to the inverse crack problem, that is the detection and reconstruction of cracks, and other defects, inside a conducting body by performing boundary measurements of current and voltage type. We formulate such an inverse problem in a free-discontinuity problems framework and propose a novel method for the numerical reconstruction of the cracks by the available boundary data. The proposed method is amenable to numerical computations and it is justified by a convergence analysis, as the error on the measurements goes to zero. We further notice that we use the Gamma-convergence approximation of the Mumford-Shah functional due to Ambrosio and Tortorelli as the required regularization term.
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