A Divergence-free Finite Element Method for Approximating the Two-dimensional Maxwell Eigenvalues from Upper

Numerical upper and lower bounds for the Maxwell eigenvalues are important in obtaining the accurate eigenvalue approximation and in the safe assessment of electromagnetism. In this paper we propose a divergence-free method using H
²
-conforming element to capture the upper bound of the Maxwell eigenvalues for a two-dimensional domain. The numerical upper bound property is asserted by the min-max principle. We prove the convergence of the proposed method and provide some numerical examples to verify the numerical upper bound property.