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Error Estimates of the Finite Element Method for Interior Transmission Problems

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Abstract

The interior transmission problem (ITP) plays an important role in the investigation of the inverse scattering problem. In this paper we propose the finite element method for solving the ITP. Based on the \(\mathbb T \)-coercivity, we derive both priori error estimate and a posteriori error estimate of the finite element approximation. Numerical experiments are also included to illustrate the accuracy of the finite element method.

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Acknowledgments

The authors thank the helpful discussions with Jin Cheng and Shuai Lu. The work is supported by the Key Project National Science Foundation of China (91130004), the Natural Science Foundation of China (11171077) and the Ministry of Education of China and the State Administration of Foreign Experts Affairs of China under a 111 project grant (B08018).

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  1. The Key Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Xinming Wu & Wenbin Chen

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  1. Xinming Wu
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  2. Wenbin Chen
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Correspondence to Wenbin Chen.

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Wu, X., Chen, W. Error Estimates of the Finite Element Method for Interior Transmission Problems. J Sci Comput 57, 331–348 (2013). https://doi.org/10.1007/s10915-013-9708-x

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  • DOI: https://doi.org/10.1007/s10915-013-9708-x

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