# Convergence of Lagrange finite elements for the Maxwell Eigenvalue Problem in 2D

@article{Boffi2020ConvergenceOL, title={Convergence of Lagrange finite elements for the Maxwell Eigenvalue Problem in 2D}, author={Daniele Boffi and Johnny Guzm{\'a}n and Michael Neilan}, journal={ArXiv}, year={2020}, volume={abs/2003.08381} }

We consider finite element approximations of the Maxwell eigenvalue problem in two dimensions. We prove, in certain settings, convergence of the discrete eigenvalues using Lagrange finite elements. In particular, we prove convergence in three scenarios: piecewise linear elements on Powell--Sabin triangulations, piecewise quadratic elements on Clough--Tocher triangulations, and piecewise quartics (and higher) elements on general shape-regular triangulations. We provide numerical experiments that… Expand

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