标题： 微分形式：拉格朗日插值、采样与多项式容许积分k-网格上的逼近 显示英文标题

标题： Differential forms: Lagrange interpolation, sampling and approximation on polynomial admissible integral k-meshes

摘要： 在这项工作中，我们处理了从通过积分定义的数据出发插值和逼近微分形式的问题。我们展示了节点插值的许多方面可以自然地推广到这个更一般的框架中；相比之下，其中一些方面需要引入几何和测度论假设。在刻画所涉及算子的范数之后，我们引入了容许积分k-网格的概念，这允许构建稳健的逼近格式，并用于提取具有高稳定性的插值集。为此，形式化了Fekete流和电流的Leja序列的概念，并提出了一个用于其逼近的数值方案。 显示英文摘要

摘要： In this work we address the problem of interpolating and approximating differential forms starting from data defined by integration. We show that many aspects of nodal interpolation can naturally be carried to this more general framework; in contrast, some of them require the introduction of geometric and measure theoretic hypotheses. After characterizing the norms of the operators involved, we introduce the concept of admissible integral k-mesh, which allows for the construction of robust approximation schemes, and is used to extract interpolation sets with high stability properties. To this end, the concepts of Fekete currents and Leja sequences of currents are formalized, and a numerical scheme for their approximation is proposed.