Use of Galerkin methods in numerical weather prediction
Williams, Roger Terry
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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.
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
NPS Report NumberNPS63-78-006
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