Use of Galerkin Methods in Numerical Weather Prediction.

Abstract

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 element methods are applied to a simple linear equation and compared. The spectral method is then applied to the nonlinear barotropic 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. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1978
Accession Number
ADA070458

Entities

People

  • R. T. Williams

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Atmospheric Sciences
  • Difference Equations
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Galerkin Method
  • Grids
  • Integrals
  • Kinetic Energy
  • Latitude
  • Longitude
  • Meteorology
  • Partial Differential Equations
  • Research Facilities
  • Shallow Water
  • Weather Forecasting

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)