High Order Biorthogonal Functions in [math](curl)

Abstract

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.