Dolomites Research Notes on Approximation

The interpolation of differential forms is a challenging problem that is getting increasing attention. The issue of finding unisolvent degrees of freedom to describe a differential form in terms of high-order Whitney forms is an active area of research nowadays. In this paper we deal with a family of such degrees of freedom, called weights, that fits with the physical and geometrical nature of the field to interpolate. These weights play the role of interpolation coefficients when reconstructing scalar/vector fields in terms of a set of selected multivariate polynomial forms. Weights are a generalization of the evaluations of a scalar function at a set of nodes in view of its reconstruction on multivariate polynomial bases. As in the nodal case, different sets of such weights are compared in terms of a Lebesgue constant. In this contribution, we briefly recall their definition and provide examples of algorithms in low dimension to compute their associated Lebesgue constant value. Insights to greater dimensions are offered as well.