A Coupled Legendre-Laguerre Spectral-Element Method for the Navier-Stokes Equations in Unbounded Domains

A Laguerre-Legendre Spectral Method for the Stokes Problem in a Semi-Infinite Channel

A mixed spectral method is proposed and analyzed for the Stokes problem in a semi-infinite channel. The method is based on a generalized Galerkin approximation with Laguerre functions in the x direction and Legendre polynomials in the y direction. The well-posedness of this method is established by deriving a lower bound on the inf-sup constant. Numerical results indicate that the derived lower...

Composite generalized Laguerre-Legendre spectral method with domain decomposition and its application to Fokker-Planck equation in an infinite channel

In this paper, we propose a composite generalized LaguerreLegendre spectral method for partial differential equations on two-dimensional unbounded domains, which are not of standard types. Some approximation results are established, which are the mixed generalized Laguerre-Legendre approximations coupled with domain decomposition. These results play an important role in the related spectral met...

A Posteriori Error Estimation of Spectral and Spectral Element Methods for the Stokes/Darcy Coupled Problem

In this paper, we carry out an a posteriori error analysis of Legendre spectral approximations to the Stokes/Darcy coupled equations. The spectral approximations are based on aweak formulation of the coupled equations by using the Beavers-JosephSaffman interface condition. The main contribution of the paper consists of deriving a number of posteriori error indicators and their upper and lower b...

A laguerre-legendre spectral-element method for the solution of partial differential equations on infinite domains: Application to the diffusion of tumour angiogenesis factors

Formulation of a Galerkin spectral element–Fourier method for three-dimensional incompressible flows in cylindrical geometries

A primitive-variable formulation for simulation of time-dependent incompressible flows in cylindrical coordinates is developed. Spectral elements are used to discretise the meridional semi-plane, coupled with Fourier expansions in azimuth. Unlike previous formulations where special distributions of nodal points have been used in the radial direction, the current work adopts standard Gauss–Lobat...