Grid Dispersion for the Spectral Element Method in Triangular Mesh

The spectral element method (SEM) is a powerful tool to study wave propagation. Its main advantages are its accuracy and efficiency. Much work has been done to study the accuracy of SEM in quadrilateral elements, but the accuracy of this method using triangular elements is not well understood. In this paper, we try to study the dispersion behaviors in triangular mesh by introducing two different types of nodes (Fekete points and Cohen points). The Fekete points are determined by minimizing the interpolation errors inside the element, while Cohen nodes are obtained by optimizing the accuracy of the quadrature rule. We analyze the grid dispersion of these two types of nodes by considering the ‘X’ type triangular mesh. The analyses are based on the plane wave assumption by solving an eigenvalue problem. Our results indicate that, considering the same polynomial order, employing Cohen nodes require more nodes per element but yield more accurate results compared to the Fekete points. Furthermore, the analysis suggests that higher order polynomials will improve the accuracy for both Fekete and Cohen nodes, which is the case for quadrilateral elements.