A Simple Finite Element Method for Meteorological Problems

A Galerkin method is applied to simple two dimensional equationsimportant in meteorological problems. The construction of thespace of trial functions for the Galerkin method is done usingthe "finite element" method, where the functions are definedas polynomials on individual elements and values are matchedon element boundaries. This method is applied to passive advectionproblems and to a non-linear gravity wave problem. The resultsare compared with those obtained by finite difference methodsand the computation time for given accuracy is shown to be atleast as short using the finite element method as with finitedifferences. Sharp local gradients are especially well handled.Extension of this approach to irregular grids and the possibleuse of higher order polynomials are proposed.