It is well known that Lagrange interpolation based on equispaced nodes can yield poor
results. Oscillations may appear when using high degree polynomials. For functions of one …

This paper deals with high order Whitney forms. We define a canonical isomorphism
between two sets of degrees of freedom. This allows to geometrically localize the classical …

Motivated by polynomial approximations of differential forms, we study analytical and
numerical properties of a polynomial interpolation problem that relies on function averages …

In this paper, we study a geometric approach for constructing physical degrees of freedom
for sequences of finite element spaces. Within the framework of finite element systems, we …

The principal aim of this work is to provide a family of unisolvent and minimal physical
degrees of freedom, called weights, for Nédélec second family of finite elements. Such …

Motivated by polynomial approximations of differential forms, we study analytical and
numerical properties of a polynomial interpolation problem that relies on function averages …

Weights are geometrical degrees of freedom that allow to generalise Lagrangian finite
elements. They are defined through integrals over specific supports, well understood in …

In this work we describe and test the construction of least squares Whitney forms based on
weights. If, on the one hand, the relevance of such a family of differential forms is nowadays …

In this article, we study the Fekete problem in segmental and combined nodal-segmental
univariate polynomial interpolation by investigating sets of segments, or segments combined …

In this work we blend interpolation theory with numerical integration, constructing an
interpolator based on integrals over $ n $-dimensional balls. We show that, under …