A new set of H(curl)-conforming hierarchical basis functions for tetrahedral meshes

A new set of H(curl)-conforming hierarchical basis functions for tetrahedral meshes is presented. Contrary to previous bases, this one is designed such that higher order basis functions vanish when they are projected onto a lower order finite-element space using the interpolation operator defined by Nedelec. Consequently, to increase the polynomial order and improve the accuracy of the interpolated field, only additional degrees of freedom (DOFs) of higher order are added, whereas the original DOFs (the coefficients for the basis functions) remain unchanged. This makes this basis very well suited for use with efficient multilevel solvers and goal-oriented hierarchical error estimators, which is demonstrated through numerical examples.