On certain configurations of points in Rn which are unisolvent for polynomial interpolation
Journal of Approximation Theory
Spectral methods on triangles and other domains
Journal of Scientific Computing
From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex
SIAM Journal on Numerical Analysis
Bounds for eigenvalues and condition numbers in the p-version of the finite element method
Mathematics of Computation
A generalized diagonal mass matrix spectral element method for non-quadrilateral elements
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Journal of Computational Physics
Tensor product Gauss-Lobatto points are Fekete points for the cube
Mathematics of Computation
An Algorithm for Computing Fekete Points in the Triangle
SIAM Journal on Numerical Analysis
On condition numbers in hp-FEM with Gauss-Lobatto-based shape functions
Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Spectral Element Methods on Unstructured Meshes: Comparisons and Recent Advances
Journal of Scientific Computing
Journal of Computational Physics
Controllability method for the Helmholtz equation with higher-order discretizations
Journal of Computational Physics
A multiscale hp-FEM for 2D photonic crystal bands
Journal of Computational Physics
Computing Fekete and Lebesgue points: Simplex, square, disk
Journal of Computational and Applied Mathematics
Hi-index | 31.47 |
In this paper, we compare a triangle based spectral element method (SEM) with the classical quadrangle based SEM and with a standard spectral method. For the sake of completeness, the triangle-SEM, making use of the Fekete points of the triangle, is first revisited. The requirement of a highly accurate quadrature rule is particularly emphasized. Then it is shown that the convergence properties of the triangle-SEM compare well with those of the classical SEM, by solving an elliptic equation with smooth (but steep) analytical solution. It is also proved numerically that the condition number grows significantly faster for triangles than for quadrilaterals. Finally, the attention is focused on a diffraction problem to show the high flexibility of the triangle-SEM.