A generalized diagonal mass matrix spectral element method for non-quadrilateral elements

Abstract

We introduce a Fekete point spectral element method. This is a generalization of the traditional quadrilateral based spectral element method to any general element such as triangles. It retains the exponential convergence and the diagonal mass matrix of the original method. We first solve a Sturm–Liouville problem in the square and the triangle to determine the correct functional space used for approximation. Once the functional space is known, we use the Fekete criterion to compute near optimal grids for these spaces which have the same number of points as the dimension of the functional space. This allows the construction of a well-behaved cardinal function basis which leads to a diagonal mass matrix.