Partially Discontinuous Nodal Finite Elements for 𝐻(curl) and 𝐻(div)

Abstract

Abstract We investigate the discretization of H ⁢ ( curl ) H(\mathrm{curl}) and H ⁢ ( div ) 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.