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 …

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 approximation by polynomials on the unit ball is studied in the frame of the Sobolev
spaces W^s_p(B^d), 1<p<∞. The main results give sharp estimates on the order of …

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 …

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 …

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 …

In this paper, we propose a space–time spectral method for solving the generalized two-
dimensional sine-Gordon equation with nonhomogeneous Dirichlet boundary conditions …

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 …

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 …

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 …