SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2331-2348, October 2024.
Abstract. From the literature, it is known that the choice of basis functions in hp-FEM heavily influences the computational cost in order to obtain an approximate solution. Depending on the choice of the reference element, suitable tensor product like basis functions of Jacobi polynomials with different weights lead to optimal properties due to condition number and sparsity. This paper presents biorthogonal basis functions to the primal basis functions mentioned above. The authors investigate hypercubes and simplices as reference elements, as well as the cases of H1 and H(Curl). The functions can be expressed as sums of tensor products of Jacobi polynomials with maximal two summands.

中文翻译：

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[math]（curl） 中的高阶双正交函数


SIAM 数值分析杂志，第 62 卷，第 5 期，第 2331-2348 页，2024 年 10 月。

抽象。从文献中可以知道，hp-FEM 中基函数的选择会严重影响计算成本，以获得近似解。根据参考元素的选择，合适的张量积（如具有不同权重的雅可比多项式的基函数）由于条件数和稀疏性而导致最佳属性。本文将双正交基函数与上述原始基函数进行了介绍。作者研究了作为参考元素的超立方体和简单体，以及 H1 和 H（Curl） 的情况。这些函数可以表示为具有最大两个求和的雅可比多项式的张量积之和。