Use of Galerkin methods in numerical weather prediction

摘要

In this report the Galerkin method is presented and the spectral and finite element methods are shown to be special cases of the general method. The spectral and finite methods are applied to a simple linear equation and compared. The spectral method is then applied to the non-linear baratropic vorticity equation in Cartesian coordinates and in spherical coordinates. The transform technique is presented which allows efficient treatment of the nonlinear terms in the spectral method. This method is also applied to the shallow water equations. The finite element method with linear basis functions is applied to the linear advection equation and compared to second and fourth order finite difference approximations. The nonlinear barotropic vorticity is also developed in finite elements.