A family of optimal Lagrange elements for Maxwell’s equations

Convergence of Lagrange Finite Element Methods for Maxwell Eigenvalue Problem in 3D

“…To the best of our knowledge, this seems to be the first paper theoretically justifying convergence of Lagrange elements on simplicial meshes in three dimensions without modifying the bilinear form. In contrast, several papers prove convergence of Lagrange elements, where they add penalization or regularization terms to the bilinear form; see [4,8,10,[16][17][18]. Parallel work by Hu et al [11,23,24] also develop finite elements on different splits with Lagrange or partially discontinuous elements while leaving the bilinear forms unchanged.…”