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arXiv · 1601.01068

Non-conforming finite element methods for transmission eigenvalue problem

Yidu Yang·Jiayu Han·Hai Bi
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Abstract

The transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory. In this paper, for the Helmholtz transmission eigenvalue problem, we give a weak formulation which is a nonselfadjoint linear eigenvalue problem. Based on the weak formulation, we first discuss the non-conforming finite element approximation, and prove the error estimates of the discrete eigenvalues obtained by the Adini element, Morley-Zienkiewicz element, modified-Zienkiewicz element et. al. And we report some numerical examples to validate the efficiency of our approach for solving transmission eigenvalue problem.

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Yidu Yang, Jiayu Han, Hai Bi. 2016-01-06. Non-conforming finite element methods for transmission eigenvalue problem. https://doi.org/10.1016/j.cma.2016.04.021

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