In this paper, we carry out a systematic comparison between the theoretical properties of Spectral Element Methods and NURBS-based Isogeometric Analysis in its basic form, that is in the framework of the Galerkin method, for the approximation of the Poisson problem, which we select as a benchmark Partial Differential Equation. Our focus is on their convergence properties, the algebraic structure and the spectral properties of the corresponding discrete arrays (mass and stiffness matrices). We review the available theoretical results for these methods and verify them numerically by performing an error analysis on the solution of the Poisson problem. Where theory is lacking, we use numerical investigation of the results to draw conjectures on the behaviour of the corresponding theoretical laws in terms of the design parameters, such as the (mesh) element size, the local polynomial degree, the smoothness of the NURBS basis functions, the space dimension, and the total number of degrees of freedom involved in the computations.

在本文中，我们以基本形式（即在Galerkin方法的框架内）对频谱元素方法和基于NURBS的等几何分析的理论性质进行了系统的比较，以选择Poisson问题。作为基准偏微分方程。我们的重点是它们的收敛特性，代数结构和相应离散阵列（质量和刚度矩阵）的光谱特性。我们回顾了这些方法的可用理论结果，并通过对泊松问题的解决方案进行了误差分析，对它们进行了数值验证。在缺乏理论的地方，我们使用结果的数值研究来根据设计参数对相应的理论定律的行为做出猜想，