9 papers
Scattered Data Histopolation in Averaging Kernel Hilbert Spaces
Ludovico Bruni Bruno, Giacomo Cappellazzo, Wolfgang Erb +1
Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of poin…
The Lebesgue constant for uniform approximation of differential forms
Ludovico Bruni Bruno, Fwderico Piazzon
In this work we address the problem of uniform approximation of differential forms starting from weak data defined by integration on rectifiable sets. We study approximation scheme…
On the conditioning of polynomial histopolation
Ludovico Bruni Bruno, Stefano Serra-Capizzano
Histopolation is the approximation procedure that associates a degree polynomial with a locally integrable function imposing tha…
A pluripotential theoretic framework for polynomial interpolation of vector-valued functions and differential forms
Ludovico Bruni Bruno, Federico Piazzon
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighte…
Sampling, approximation, and interpolation of differential forms by admissible integral k-meshes
Ludovico Bruni Bruno, Federico Piazzon
In this work we introduce the concept of admissible integral -mesh for sampling differential forms with contiuous coefficients on a real body , and provide two te…
A least squares approach to Whitney forms
Ludovico Bruni Bruno, Giacomo Elefante
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 now…
Interpolation by integrals on balls
Ludovico Bruni Bruno, Giacomo Elefante
In this work we blend interpolation theory with numerical integration, constructing an interpolator based on integrals over -dimensional balls. We show that, under hypotheses on…
Polynomial Interpolation of Function Averages on Interval Segments
Ludovico Bruni Bruno, Wolfgang Erb
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages ov…
Unisolvent and minimal physical degrees of freedom for the second family of polynomial differential forms
Ludovico Bruni Bruno, Enrico Zampa
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 elem…