Flexible Weights for High Order Face Based Finite Element Interpolation

We are interested in the high order interpolation of physical fields in the space of Nédélec first family face based finite elements for simplicial meshes. As degrees of freedom, we adopt the weights, that are the fluxes of the field under consideration through a distribution of 2-simplices in each tetrahedron of the mesh. The flexibility with respect to the choice of the support for these degrees of freedom allows to consider nonuniform distributions. We analyse and compare the quality of the interpolation on uniform and nonuniform distributions of 2-simplices in terms of the generalised Lebesgue constant.