Spectral element methods on unstructured meshes: which interpolation points?

Authors:
Richard Pasquetti;Francesca Rapetti
Affiliations:
J.A. Dieudonné, U.M.R. 6621, C.N.R.S., Université de Nice Sophia-Antipolis, Nice cedex 02, France 06108;J.A. Dieudonné, U.M.R. 6621, C.N.R.S., Université de Nice Sophia-Antipolis, Nice cedex 02, France 06108
Venue:
Numerical Algorithms
Year:
2010

Citing 15
Cited 3

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
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)
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
Nodal high-order methods on unstructured grids

Journal of Computational Physics
On condition numbers in hp-FEM with Gauss-Lobatto-based shape functions

Journal of Computational and Applied Mathematics
Improved Lebesgue constants on the triangle

Journal of Computational Physics
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
Nodal configurations and voronoi tessellations for triangular spectral elements

Nodal configurations and voronoi tessellations for triangular spectral elements
Overlapping Schwarz Methods for Fekete and Gauss-Lobatto Spectral Elements

SIAM Journal on Scientific Computing
Polymorphic nodal elements and their application in discontinuous Galerkin methods

Journal of Computational Physics
Computing approximate Fekete points by QR factorizations of Vandermonde matrices

Computers & Mathematics with Applications

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
A new triangular spectral element method I: implementation and analysis on a triangle

Numerical Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

In the field of spectral element approximations, the interpolation points can be chosen on the basis of different criteria, going from the minimization of the Lebesgue constant to the simplicity of the point generation procedure. In the present paper, we summarize some recent nodal distributions for a high order interpolation in the triangle. We then adopt these points as approximation points for the numerical solution of an elliptic partial differential equation on an unstructured simplicial mesh. The L 2-norm of the approximation error is then analyzed for a model problem.