Error Estimates of the Finite Element Method for Interior Transmission Problems

Authors:
Xinming Wu;Wenbin Chen
Affiliations:
The Key Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, People's Republic of China 200433;The Key Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, People's Republic of China 200433
Venue:
Journal of Scientific Computing
Year:
2013

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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.