A spectral-element method based on the Legendre–Galerkin approximation is presented to
solve the two-dimensional biharmonic equations. Rigorous error analysis is carried out to …

Abstract The Kuramoto‐Sivashinsky equation has emerged as a fundamental evolution
equation to describe highly nonlinear physical processes in unstable systems. In general, it …

In this paper, we propose a new Galerkin spectral element method for one-dimensional
fourth-order boundary value problems. We first introduce some quasi-orthogonal …

We propose an efficient algorithm based on the Legendre–Galerkin approximation for the
direct solution of the Cahn–Hilliard equation with homogeneous and nonhomogeneous …

We propose an efficient algorithm based on the Legendre–Galerkin approximations for the
direct solution of the biharmonic eigenvalue problems with the boundary conditions of the …

Under simply supported plate (SSP) boundary conditions, a numerical method based on the
higher-order Legendre polynomial approximation was studied and developed for fourth …

An efficient Legendre–Galerkin spectral element method for the steady flows in rectangular
cavities is proposed in this paper. Firstly, we eliminate the singularity of biharmonic equation …

In this work, an efficient Legendre spectral element method was proposed to solve the two‐
dimensional Stokes eigenvalue problem on L‐shaped domain. Based on minimax principle …