Non-conforming finite element methods for transmission eigenvalue problem
Numerical Analysis
2016-06-29 v1
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.
Cite
@article{arxiv.1601.01068,
title = {Non-conforming finite element methods for transmission eigenvalue problem},
author = {Yidu Yang and Jiayu Han and Hai Bi},
journal= {arXiv preprint arXiv:1601.01068},
year = {2016}
}