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
Spectral collocation on triangular elements
Journal of Computational Physics
Spectral schemes on triangular elements
Journal of Computational Physics
An Algorithm for Computing Fekete Points in the Triangle
SIAM Journal on Numerical Analysis
TRIANGULAR SPECTRAL ELEMENTS FOR INCOMPRESSIBLE FLUID FLOW
TRIANGULAR SPECTRAL ELEMENTS FOR INCOMPRESSIBLE FLUID FLOW
Performance of numerically computed quadrature points
Applied Numerical Mathematics
Spectral element methods on unstructured meshes: which interpolation points?
Numerical Algorithms
Computing Fekete and Lebesgue points: Simplex, square, disk
Journal of Computational and Applied Mathematics
On the generation of symmetric Lebesgue-like points in the triangle
Journal of Computational and Applied Mathematics
Radial orthogonality and Lebesgue constants on the disk
Numerical Algorithms
| Hi-index | 31.45 |
New sets of points with improved Lebesgue constants in the triangle are calculated. Starting with the Fekete points a direct minimization process for the Lebesgue constant leads to better results. The points and corresponding quadrature weigths are explicitly given. It is quite surprising that the optimal points are not symmetric. The points along the boundary of the triangle are the 1D Gauss-Lobatto points. For all degrees, our points yield the smallest Lebesgue constants currently known. Numerical examples are presented, which show the improved interpolation properties of our nodes.