To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness of the approach. The finite element method is one of the popular tools for the numerical resolution of a wide range of PDEs. The purpose of this document is to provide the formal proof community with very detailed pen-and-paper proofs for the construction of the Lagrange finite elements of any degree on simplices in positive dimension.

翻译：为确保偏微分方程数值模拟程序正确性的最高置信度，必须将用于确立方法可靠性的数学概念与结论进行形式化。有限元方法是广泛应用于各类偏微分方程数值求解的主流工具之一。本文旨在为形式化验证领域提供极其详尽的手写证明，阐述任意阶次拉格朗日有限元在正维单纯形上的构造过程。