A three-dimensional spectral element model for the solution of the hydrostatic primitive equations
Journal of Computational Physics
A Discontinuous Spectral Element Method for the Level Set Equation
Journal of Scientific Computing
Spectral element methods on triangles and quadrilaterals: comparisons and applications
Journal of Computational Physics
A nodal triangle-based spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
Improved Lebesgue constants on the triangle
Journal of Computational Physics
Spectral Element Methods on Unstructured Meshes: Comparisons and Recent Advances
Journal of Scientific Computing
Journal of Computational Physics
Spectral difference method for unstructured grids I: basic formulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Performance of numerically computed quadrature points
Applied Numerical Mathematics
Asymmetric cubature formulas for polynomial integration in the triangle and square
Journal of Computational and Applied Mathematics
A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates
Journal of Computational Physics
Computing approximate Fekete points by QR factorizations of Vandermonde matrices
Computers & Mathematics with Applications
Least-squares polynomial approximation on weakly admissible meshes: Disk and triangle
Journal of Computational and Applied Mathematics
Spectral element methods on unstructured meshes: which interpolation points?
Numerical Algorithms
Computing Multivariate Fekete and Leja Points by Numerical Linear Algebra
SIAM Journal on Numerical Analysis
An eigen-based high-order expansion basis for structured spectral elements
Journal of Computational Physics
Computing Fekete and Lebesgue points: Simplex, square, disk
Journal of Computational and Applied Mathematics
Symmetric quadrature rules for tetrahedra based on a cubic close-packed lattice arrangement
Journal of Computational and Applied Mathematics
On the generation of symmetric Lebesgue-like points in the triangle
Journal of Computational and Applied Mathematics
Journal of Computational Physics
The generation of arbitrary order curved meshes for 3D finite element analysis
Computational Mechanics
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On the line and its tensor products, Fekete points are known to be the Gauss--Lobatto quadrature points. But unlike high-order quadrature, Fekete points generalize to non-tensor-product domains such as the triangle. Thus Fekete points might serve as an alternative to the Gauss--Lobatto points for certain applications. In this work we present a new algorithm to compute Fekete points and give results up to degree 19 for the triangle. For degree d 10 these points have the smallest Lebesgue constant currently known. The computations validate a conjecture of Bos [ J. Approx. Theory, 64 (1991), pp. 271--280] that Fekete points along the boundary of the triangle are the one-dimensional Gauss--Lobatto points.