Spectral element methods on triangles and quadrilaterals: comparisons and applications
Journal of Computational Physics
Short Note: An explicit expression for the penalty parameter of the interior penalty method
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
High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids
Journal of Computational Physics
Spectral difference method for unstructured grids I: basic formulation
Journal of Computational Physics
Idempotent filtering in spectral and spectral element methods
Journal of Computational Physics
A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equations
Journal of Computational Physics
Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations
Journal of Scientific Computing
Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Performance of numerically computed quadrature points
Applied Numerical Mathematics
A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates
Journal of Computational Physics
Polymorphic nodal elements and their application in discontinuous Galerkin methods
Journal of Computational Physics
Computational cost of the Fekete problem I: The Forces Method on the 2-sphere
Journal of Computational Physics
Journal of Computational Physics
Higher-order Finite Elements for Hybrid Meshes Using New Nodal Pyramidal Elements
Journal of Scientific Computing
Journal of Computational Physics
Spectral element methods on unstructured meshes: which interpolation points?
Numerical Algorithms
Applied Numerical Mathematics
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
Efficient simulation of cardiac electrical propagation using high order finite elements
Journal of Computational Physics
Symmetric quadrature rules for tetrahedra based on a cubic close-packed lattice arrangement
Journal of Computational and Applied Mathematics
Radial orthogonality and Lebesgue constants on the disk
Numerical Algorithms
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The electrostatic interpretation of the Jacobi--Gauss quadrature points is exploited to obtain interpolation points suitable for approximation of smooth functions defined on a simplex. Moreover, several new estimates, based on extensive numerical studies, for approximation along the line using Jacobi--Gauss--Lobatto quadrature points as the nodal sets are presented.The electrostatic analogy is extended to the two-dimensional case, with the emphasis being on nodal sets inside a triangle for which two very good matrices of nodal sets are presented. The matrices are evaluated by computing the Lebesgue constants and they share the property that the nodes along the edges of the simplex are the Gauss--Lobatto quadrature points of the Chebyshev and Legendre polynomials, respectively. This makes the resulting nodal sets particularly well suited for integration with conventional spectral methods and supplies a new nodal basis for h-p finite element methods.