High-order vector bases for computational electromagnetics

Summary form only given. New families of hierarchical curl and divergence-conforming vector bases for the most commonly used two - and three-dimensional cells are directly constructed from orthogonal scalar polynomials to enhance their linear independence, which is a simpler process than an orthogonalization applied to the final vector functions. These functions span the mixed-order (or reduced) spaces of Nédélec and can be used to deal with structures meshed by a mixture of cells of different geometry.