Continuous Finite Element Method For Maxwell Eigenvalue Problems With Regular Decomposition Technique

With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; \Omega)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high order regular decomposition, a novel numerical method using standard high order Lagrange finite elements is designed for solving Maxwell eigenvalue problems. Specifically, the full convergence orders of the eigenpair approximations are proved for the proposed numerical method. Finally, numerical examples are provided to validate the proposed scheme and confirm the theoretical convergence results.