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
An Algorithm for Computing Fekete Points in the Triangle
SIAM Journal on Numerical Analysis
Spectral collocation schemes on the unit disc
Journal of Computational Physics
Spectral Element Methods on Unstructured Meshes: Comparisons and Recent Advances
Journal of Scientific Computing
Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials
Journal of Scientific Computing
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
A Triangular Spectral Element Method Using Fully Tensorial Rational Basis Functions
SIAM Journal on Numerical Analysis
Gauss quadrature routines for two classes of logarithmic weight functions
Numerical Algorithms
Spectral element methods on unstructured meshes: which interpolation points?
Numerical Algorithms
Journal of Computational Physics
Spectral Methods: Algorithms, Analysis and Applications
Spectral Methods: Algorithms, Analysis and Applications
On Gauss-Lobatto Integration on the Triangle
SIAM Journal on Numerical Analysis
To CG or to HDG: A Comparative Study
Journal of Scientific Computing
Hi-index | 0.00 |
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle---triangle mapping proposed in the conference note (Li et al. 2011). Here, we provide some new insights into the originality and distinctive features of the mapping, and show that this transform only induces a logarithmic singularity, which allows us to devise a fast, stable and accurate numerical algorithm for its removal. Consequently, any triangular element can be treated as efficiently as a quadrilateral element, which affords a great flexibility in handling complex computational domains. Benefited from the fact that the image of the mapping includes the polynomial space as a subset, we are able to obtain optimal L2- and H1-estimates of approximation by the proposed basis functions on triangle. The implementation details and some numerical examples are provided to validate the efficiency and accuracy of the proposed method. All these will pave the way for developing an unstructured TSEM based on, e.g., the hybridizable discontinuous Galerkin formulation.