Non-conforming finite element methods for transmission eigenvalue problem ☆

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, the Morley–Zienkiewicz element, the 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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