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 …

With the gap between processor clock speeds and memory bandwidth speeds continuing to
increase, the use of arithmetically intense schemes, such as high-order finite element …

This paper presents a practical algorithm for constructing high order discontinuous Galerkin
spectral element methods (DGSEM) on mixed triangular and quadrilateral grids. The …

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

A triangular spectral element method is proposed for Stokes eigenvalues, which utilizes the
generalized orthogonal Koornwinder polynomials as the local basis functions. The local …

The airborne transient electromagnetics method has been widely used in geophysical
exploration in recent years, but it still faces challenges in balancing the accuracy and …

Abstract The Ladyženskaja–Babuška–Brezzi (LBB) condition is a necessary condition for
the well-posedness of discrete saddle point problems stemming from discretizing the Stokes …

A weak Galerkin spectral element method is proposed to solve second order partial
differential equations. Following the idea of the weak Galerkin finite element method, this …

Abstract The multidomain Legendre–Galerkin Chebyshev-collocation method is considered
to solve one-dimensional linear evolution equations with two nonhomogeneous jump …

We develop an H m-conforming (m≥ 1) spectral element method on multi-dimensional
domain associated with the partition into multi-dimensional rectangles. We construct a set of …