Partially discontinuous nodal finite elements for $H(\mathrm{curl})$ and $H(\mathrm{div})$

Abstract: We investigate discretization of $H(\mathrm{curl})$ and $H(\mathrm{div})$ in two and three space dimensions by partially discontinuous nodal finite elements, i.e., vector-valued Lagrange finite elements with discontinuity in certain directions. These spaces can be implemented as a combination of continuous and discontinuous Lagrange elements and fit in de~Rham complexes. We construct well-conditioned nodal bases.