[HTML][HTML] On Sobolev orthogonal polynomials
F Marcellán, Y Xu - Expositiones Mathematicae, 2015 - Elsevier
Sobolev orthogonal polynomials have been studied extensively in the past quarter-century.
The research in this field has sprawled into several directions and generates a plethora of …
The research in this field has sprawled into several directions and generates a plethora of …
Some progress in spectral methods
BY Guo - Science China Mathematics, 2013 - Springer
In this paper, we review some results on the spectral methods. We first consider the Jacobi
spectral method and the generalized Jacobi spectral method for various problems, including …
spectral method and the generalized Jacobi spectral method for various problems, including …
Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle
Spectral approximations on the triangle by orthogonal polynomials are studied in this paper.
Optimal error estimates in weighted semi-norms for both the $ L^ 2-$ and $ H^ 1_0 …
Optimal error estimates in weighted semi-norms for both the $ L^ 2-$ and $ H^ 1_0 …
An eigen-based high-order expansion basis for structured spectral elements
We present an eigen-based high-order expansion basis for the spectral element approach
with structured elements. The new basis exhibits a numerical efficiency significantly …
with structured elements. The new basis exhibits a numerical efficiency significantly …
New triangular mass-lumped finite elements of degree six for wave propagation
WA Mulder - Progress In Electromagnetics Research, 2013 - jpier.org
Mass-lumped continuous finite elements allow for explicit time stepping with the second-
order wave equation if the resulting integration weights are positive and provide sufficient …
order wave equation if the resulting integration weights are positive and provide sufficient …
[HTML][HTML] Space–time spectral method for the two-dimensional generalized sine-Gordon equation
W Liu, J Sun, B Wu - Journal of Mathematical Analysis and applications, 2015 - Elsevier
In this paper, we propose a space–time spectral method for solving the generalized two-
dimensional sine-Gordon equation with nonhomogeneous Dirichlet boundary conditions …
dimensional sine-Gordon equation with nonhomogeneous Dirichlet boundary conditions …
Error estimates for the scaled boundary finite element method
KO Coelho, PRB Devloo, SM Gomes - Computer Methods in Applied …, 2021 - Elsevier
Abstract The Scaled Boundary Finite Element Method (SBFEM) is a technique in which
approximation spaces are constructed using a semi-analytical approach. They are based on …
approximation spaces are constructed using a semi-analytical approach. They are based on …
Efficient tensor-product spectral-element operators with the summation-by-parts property on curved triangles and tetrahedra
We present an extension of the summation-by-parts (SBP) framework to tensor-product
spectral-element operators in collapsed coordinates. The proposed approach enables the …
spectral-element operators in collapsed coordinates. The proposed approach enables the …
H()-conforming quadrilateral spectral element method for quad-curl problems
In this paper, we propose an H (curl 2)-conforming quadrilateral spectral element method to
solve quad-curl problems. Starting with generalized Jacobi polynomials, we first introduce …
solve quad-curl problems. Starting with generalized Jacobi polynomials, we first introduce …